- Click hereto get an answer to your question ️ If in two triangles PQR and DEF , PR = EF , QR = DE and PQ = FD , then PQR
- In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then a) ∆DEF ≅ ∆PQR b) ∆FED ≅ ∆PRQ shweta9549309922 shweta9549309922 05.08.202
- in two triangles def and pqr, if de =qr, ef =pr and fd =pq then - 3105837

In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ. then. ∆DEF ≅ ∆PQR ∆FED≅ ∆PRQ; ∆EDF ≅ ∆RPQ ∆EFD≅ ∆PQR Explanation. First, we could try this: Drawing a diagram. I will attach a diagram here. So please refer to the attachment. Extra explanation. DE = QR, EF = PR. We can see that point E is common In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then - 2475459 If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar. Here, the include angle are with DEAB. . =F DBC. . is ∠B=∠D . So, the two triangle are similar, when ∠B=∠D . Hence, the correct answer is option (C) MCQ Questions & Answers from CBSE Class 9 Maths Chapter 7 Triangles are given below: Q1. In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then. a) ∆DEF ≅ ∆PQR. b) ∆FED ≅ ∆PRQ

Now draw two triangles with the help of given conditions:-Here and {Given} {by AA similarity} {corresponding angles of similar triangles} Here option (A) is true because both the terms are derived from equation (1) Here option (B) is not true because the first term is not derived from equation (1 ** Given: ∆DEF and ∆PQR, ∠D = ∠Q, ∠R = ∠E**. As we know that if two corresponding angles of two triangles are congruent then both the triangles are similar because if two angle pairs are the equal then the third angle must also be equal. So, by AAA similarity criteria, ∴ ∆DEF ∼ ∆QRP ⇒ ∠F = ∠P [corresponding angles of. State the congruence in the symbolic form of **two** **triangles** **PQR** **and** **DEF** , if PR=EF , QR=DE and PQ=FD - Maths - **Triangles**. NCERT Solutions; Board Paper Solutions abc and **triangle** **d** **e** f ab is equal to **FD** angle a is equal to angle D state the necessary condition according to which **two** **triangles** will be congruant by sas-3 ; Hlo students, The. In Fig. 7.10 PQR, if ∠Q =40° and ∠R = 72°, then find the shortest and the largest sides of the triangle. asked Sep 20, 2018 in Class IX Maths by aditya23 ( -2,137 points) triangles In ∆DEF and ∆PQR ∠D ≅ ∠Q ∠R ≅ ∠E By AA test of similarity ∆DEF~ ∆PQR \[\therefore \frac{DE}{PQ} = \frac{EF}{QR} = \frac{DF}{PR} \left( \text.

For two triangles, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle. In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then a) ∆DEF ≅ ∆PQR b) ∆FED ≅ ∆PRQ c) ∆EDF ≅ ∆RPQ d) ∆PQR ≅ ∆EFD. In triangles ABC and DEF, AB = FD and ∠A. * Here, ∆ PQR ∼ ∆ DEF as*. PQ / DE = QR / EF = RP / FD (2) Side-Angle-Side (SAS) criterion for similarity: If the corresponding two sides of the two triangles are proportional and one included angle is equal to the corresponding included angle of another triangle then the triangles are similar. Here, ∆ LMN ∼ ∆ QRS in which. ∠L = ∠ (i) If_____sides of a triangle are respectively equal to the three sides of the other triangle, then the triangles are congruent. (l) If in two triangles PQR and DEF, PR = EF, QR = DE and PQ = FD, then ΔPQR Δ_____. (m) Sum of any two sides of a triangle is_____than the third side. (n) If two angles of a triangle are unequal, then the smaller. Solution : Question 4: ∆PQR ~ ∆DEF for the correspondence PQR ↔ EDF. If PQ + QR = 15, DE + DF = 10 and PR = 6, find EF. Solution : Question 5: In ∆ABC and ∆PQR, ABC ↔ QPR is a similarity. The perimeter of ∆ABC is 15 and perimeter of ∆PQR is 27. If BC = 7 and QR = 9, find PR and AC

- In triangles ABC and DEF, B = E, F = C and AB = 3 DE. Then, the two triangles are (A) congruent but not similar (B) similar but not congruent (C) neither congruent nor similar (D) congruent as well as similar Q.6 The perimeters of two similar triangles ABC and PQR are respectively 36cm and 48cm
- DE = AB . FD. 4.) If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ ,then (A) ∆PQR ~ ∆CAB (B) ∆PQR ~ ∆ABC (C) ∆CBA ~ ∆PQR (D) ∆BCA ~ ∆PQR. 5.) If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true? (A) EF/PR = DF/PQ (B) DE/PQ = EF/RP (C) DE/QR = DF/PQ (D) EF/RP = DE/QR
- e whether the two triangles are congruent or not, using RHS congruence rule. In the case of congruent triangles, write the result in symbolic form: ΔABC. ΔPQR. (i) ∠B = 90°, AC = 8 cm, AB = 3 cm. (i) ∠P = 90°, PR = 3 cm, QR = 8 cm
- Students can solve NCERT Class 10 Maths Triangles MCQs with Answers to know their preparation level. Class 10 Maths MCQs Chapter 6 Triangles. 1. O is a point on side PQ of a APQR such that PO = QO = RO, then. (a) RS² = PR × QR. (b) PR² + QR² = PQ². (c) QR² = QO² + RO². (d) PO² + RO² = PR². Answer

If in two ∆DEF and ∆PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true? asked Aug 26, 2020 in Triangles by Shyam01 ( 50.4k points) triangles 2. Two poles 6m and 1 1m high stands vertically on the ground If the distance between their feet is 12m, then the distance between their tops is: (A) 1 1m (B) 12 m (C) 13 m (D) 14m 3. If in two triangles DEF and PQR, ∠D = ∠Q, ∠R = ∠E, which of the following is not true? (A) DE EF PQ RP = (B) EF DF PR PQ = (C) DE DF QR PQ = (D) EF DE RP. 60 seconds. Report an issue. Q. In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are: answer choices. Isosceles but not congruent. Isosceles and congruent. Congruent but not isosceles * If ABC and DEF are two triangles such that AB/DE = BC/EF = CA/FD = 3/4 , then write Area ( ABC): Area ( DEF)*. asked Apr 27 in Triangles by Saadah ( 31.3k points) triangles

Question 1: Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles. Answer: Let ABC and PQR be two right triangles with AB ⊥ BC and PQ ⊥ QR. Given: BC = 9, AB = 5, PQ = 6 and QR = 10. ∴ A ( ABC) A ( PQR) = AB × BC PQ × QR = 5 × 9 6 × 10 = 3 4 In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is : (a) 6 cm (b) 8 cm (c) 7 cm (d) 10 cm. Answer. Answer: (b) 8 c The two triangles will be congruent by SAS axiom if [1] (a) BC QR = (b) AC PR = (c) AB QR = (d) None of these Ans : (a) BC QR = Given, AB PQ = B + Q + = Download 20 Solved Sample Papers pdfs from or Page 2 Mathematics IX Solved Sample Paper 7 In order for ABC T to be congruent to PQR T by SAS axiom corresponding sides BC and QR should be equal Q6. In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is : (a) 6 cm (b) 8 cm (c) 7 cm (d) 10 c In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then a) ∆DEF ≅ ∆PQR b) ∆FED ≅ ∆PRQ c) ∆EDF ≅ ∆RPQ d) ∆PQR ≅ ∆EFD Answer: (b) Q2. In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to: a) 80o b) 40o c) 50o d) 100o Answer: (c) Q3. Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the.

- Click hereto get an answer to your question ️ If in two triangles Δ ABC and Δ PQR , AB = QR, BC = PR and CA = PQ, then
- In two triangles DEF and PQR, if DE = QR, EF = PR and FD = PQ, then a) ∆DEF ≅ ∆PQR b) ∆FED ≅ ∆PRQ c) ∆EDF ≅ ∆RPQ d) ∆PQR ≅ ∆EFD Q2. In ∆A , = A and ∠B = 80°. Then ∠A is equal to: a) 80o b) 40o c) 50o d) 100o Q3. Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the third side of the triangle.
- In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. Then, the two triangles are asked Aug 18, 2018 in Mathematics by AbhinavMehra ( 22.5k points
- Click hereto get an answer to your question ️ 4. If in two triangles ABC and PQR (A) \( \Delta \mathrm { PQR } \sim \Delta \mathrm { CAB } \) \( ( C ) \Delta C.

In two triangles ABC and PQR AB/PQ = BC/QR. For similarity of two triangles which angles should name them and also given reason for your answer. BC = PR and CA = PQ then : (A) ∆ABC ≅ ∆PQR. asked May 15, 2020 in Similarity by RupamBharti (36 class-10; 0 votes. 1 answer. In triangles ABC and DEF, AB = FD and ∠A = ∠D. Two. Sample Question 1: In the two triangles ABC and DEF, AB = DE and AC = EF. Name two angles from the two triangles that must be equal so that the two triangles are congruent. Give reason for your answer. Solution: The required two angles are ∠A and ∠E. When ∠A = ∠E, ∆ ABC ≅ ∆ EDF by SAS criterion Class 9 Maths Chapter 7 Triangles | Multiple Choice Questions. 1. Two figures are ———, if they are of the same shape and of the same size. 2. Angles opposite to equal sides of a triangle are ————-. 3. Each angle of an equilateral triangle is of ———- degree. 4. In a triangle, angle opposite to the longer side i CBSE Class 10 Math 2 Marks Questions Triangles. 1. In figure PQ | | CD and PR | | CB. Prove that. 2. If figure two triangles ABC and DBC are on the same base BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE × CE = BE × DE. 3. Find the perimeter of rhombus whose diagonals are 20 cm & 30 cm

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students AB/DE = BC/EF = CA/FD = [AB + BC +CA] / [DE + EF + FD] 4. The ratio of the area of two similar triangles are equal to the ratio of the squares of their corresponding sides. 5. If two triangles have common vertex and their bases are on the same straight line, the ratio between their areas is equal to the ratio between the length of their bases. Rajasthan Board RBSE Class 10 Maths Chapter 11 Similarity Ex 11.3. Question 1. In two triangles ABC and PQR [latex]\frac { AB } { PQ } [/latex] = [latex]\frac { BC } { QR } [/latex]. For similarity of two triangles which angles should be equal, (RBSESolutions.com) name them and also given reason for your answer In ∆PQR, if PS SQ = PT TR, , then ST || QR. l If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion). 6. TRIANGLES l If in two triangles, two angles of one triangle are respectively equal to the two angles of the othe

**In** **triangle** **PQR** length of the side **QR** is less than twice the length of the side PQ by 2 cm. Length of the side **PR** exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the **triangle** **PQR** is : (a) 6 cm (b) 8 cm (c) 7 cm (d) 10 cm. Answer. Answer: (b) 8 c and in ∆DEF, DE = 2.3, EF = 5 and FD = 4. Question 8. In ∆PQR, M and N are points on sides PQ and PR respectively such that PM = 15 cm and NR = 8 cm. If PQ = 25 cm and PR = 20 cm. state whether MN || QR. Solution: In ∆PQR, P and Q are points on PQ and PR such that PM = 15 cm, NR = 8 cm PQ = 25 cm and PR = 20 cm PN = PR - NR = 20 - 8.

Here are two triangles ABC and PQR. It is given. AB=PQ. ∠B= ∠P. BC=PR. So, two sides are equal, and angle between these two equal sides are equal, therefore, both the triangles are concurrent by Side Angle Side (SAS) Criteria. Here, option (A) is correct. Q5. In triangle ABC and PQR, if ∠A=∠R, ∠B=∠P and AB=RP Maharashtra State Board Class 10 Maths Solutions Chapter 1 Similarity Problem Set 1. Question 1. Select the appropriate alternative. i. In ∆ABC and ∆PQR, in a one to one correspondence = = , then. ii. If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E, then which of the following statements is false? ∆DEF ~ ∆QRP . [AA test of. Triangles 1. O is a point on side PQ of a APQR such that PO = QO = RO, then (a) RS² = PR × QR (b) PR² + QR² = PQ² (c) QR² = QO² + RO² (d) PO² + RO² = PR 15. If two angles of a triangle are 60° each, then the triangle is (a) Isosceles but not equilateral (b) Scalene (c) Equilateral (d) Right-angled 16. The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is (a) 120 cm (b) 122 cm (c) 71 cm (d) 142 cm 17. In ∆ PQR, if PQ = QR and ∠Q = 100°, then ∠ R is equal t ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity MCQS. ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Chapter Test. Choose the correct answer from the given four options (1 to 22): Question 1. In the given figure, ∆ABC ~ ∆QPR. Then ∠R is. (a) 60°. (b) 50°. (c) 70°

Examine each pair of triangles in Figure, and state which pair of triangles are similar. Also, state the similarity criterion used by you for answering the question and write the similarity relation in symbolic for Chapter 3 Triangles In PQR Given PQ = 12 QR = 5 Q = 90˚ PR2 = PQ2+QR2 [Pythagoras theorem] PR2 = 122+52 PR2 = 144+25 = 169 Taking square root PR = √169 = 13 In a right angled triangle, the length of the median on its hypotenuse is half the length of the hypotenuse. QS = ½ PR = ½ ×13 = 6.5 l(QS) is 6.5 units. 4 NCERT Solutions for Class 10 Maths Chapter 6 Triangles. Answer : (i)Two Equilateral Triangle and Two Rectangle. (ii) 1)Triangle and rhombus. 2)Rectangle and circle. Q3 ) State whether the following quadrilaterals are similar or not : NCERT Solutions for Class 10 Maths Chapter 6 Triangles. Answer : From the given two figures, we can see their. If the altitudes from two vertices of a triangle to the opposite sides are equal then the triangle is (a) equilateral (b) isosceles (c) scalene (d) right angled 15. In ABC 3 and DEF 3 , it is given that AB DE and BC EF

- PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then If ABC and DEF are two triangles such that AC = 2.5 cm, BC = 5 cm,.
- D. 100 o. 3. Two sides of a triangle are of length 5 cm and 1.5 cm. The length of the third side of the triangle cannot be: A. 3.6 cm. B. 4.1 cm
- The area of two similar triangles DPQR and DXYZ are 144 cm2 and 49 cm2 respectively. If the shortest side of larger ΔPQR be 24 cm, then the shortest side of the smaller triangle ΔXYZ is (a) 7 c
- From ∆ABC and ∆PQR, we have, AB/QR = BC/PR = CA/PQ. If sides of one triangle are proportional to the side of the other triangle, and their corresponding angles are also equal, then both the triangles are similar by SSS similarity

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Problem Set 1 Geometry 10th Class Maths Part 2 Answers Solutions Chapter 6 Statistics.. Problem Set 1 Geometry 10th Std Maths Part 2 Answers Chapter 1 Similarity. Question 1. Select the appropriate alternative. i. In ∆ABC and ∆PQR, in a one to one correspondence \(\frac { AB }{ QR } \) = \(\frac { BC }{ PR } \) = \(\frac. We know that two triangles are similarity of their corresponding angles are equal and corresponding sides are proportional. (i) In ∆ABC and ∆PQR In ∆PQR, PQ = 4.5 cm, QR = 6 cm. ⇒ AF x FB = EF x FD. Hence proved. Question 12. Solution: Given : In the given figure NCERT Solutions Class 10 Maths Chapter 6, Triangle, is part of the Unit Geometry which constitutes 15 marks of the total marks of 80. On the basis of the CBSE Class 10 syllabus, this chapter belongs to the unit that has the second-highest weightage. Hence, having a clear understanding of the concepts, theorems and the problem-solving methods in. Here, the corresponding two sides and the perimeters of two triangles are proportional, then third side of both triangles will also in proportion. Question 8: If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle

Triangle LMN is the required triangle. A triangle PQR has the measurements PQ = 6 cm, QR = 4.5 cm and RP = 5 cm. Which among the following is the first step of construction? (A) With P as the centre and radius 5 cm, draw an arc. (B) Draw a line segment PQ of length 6 cm To prove two triangles congruent, We use SAS Criteria - Side Angle Side. In SAS Congruency Criteria, 2 sides of both the triangles are equal. 1 angle between these side of both the triangles are equal. For example. Here, 2 sides and the angle between them are equal. Let's do some examples Rajasthan Board RBSE Class 10 Maths Chapter 11 Similarity Ex 11.3. Question 1. In two triangles ABC and PQR = . For similarity of two triangles which angles should be equal, (RBSESolutions.com) name them and also given reason for your answer. ∴ ∠B = ∠Q is essential for similarity of two triangles

- In Δ PQR, if ∠ R > ∠ Q, then (A) QR > PR (B) PQ > PR (C) PQ < PR (D) QR < PR 10. In triangles ABC and PQR, AB = AC, ∠ C = ∠ P and ∠ B = ∠ Q. The two triangles are (A) isosceles but not congruent (B) isosceles and congruent (C) congruent but not isosceles (D) neither congruent nor isosceles 11. In triangles ABC and DEF, AB = FD and.
- Given two triangles are congruent then we can write : (d) none of these. Answer. These figures show that the three sides of one triangle are equal to the three sides of the other triangle. So by SSS congruency rule, the two triangles are congruent. It can easily seen that A <-> R, B <-> P and C <-> Q
- ∆ABC and ∆PQR are two similar triangles (RBSESolutions.com) whose areas are 100 cm 2 and 144 cm 2 and height of ∆ABC is 6 cm. then height of ∆PQR will be : (A) 12 cm (B) 6.3 c
- Criteria For Similarity Of Triangles. AAA similarity criterion: If in two triangles, corresponding angles are equal, then the triangles are similar. AA Similarity criterion: If in two triangles, two angles of one triangle are respectively equal the two angles of the other triangle, then the two triangles are similar. SSS Similarity criterion: If in two triangles, corresponding sides are in the.
- (AB / DE) = (BC / EF) = (CA / FD) then the two triangles are similar (see Fig. 6.22). Fig. 6.22 t must be noted that as done in the case of congruency of two triangles, the similarity of two triangles should also be expressed symbolically, using correct correspondence of their vertices

Answer to: Triangle PQR is similar to triangle DEF, PQ = 4 cm, DE = 6 cm, P R = x 2 , D F = 24 x 2 What is the length of DF? By signing up,.. Two triangles are similarity of their corresponding angles are equal and corresponding sides are DF = 3 and EF = 2 PQ = 4, PR = 6 and QR = 5 DE/QR = 2.5/5 = 1/2 DF/PR = 3/6 = 1/2 and EF/PQ = 2/4 = 1/2 ∆DEF ~ ∆PQR (By SSS) RS Aggarwal Solutions for Class 10 Maths Chapter In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is Chapter 6 TRIANGLES NCERT Class 10 Mathematics For Blind and Visually Impaired students by Dr T K Bansal This Chapter is planned, organized and described by Dr. T K Bansal for visually impaired and blind students. All efforts have been made to make the chapter fully accessible by providing headings, describing figures and tables. The Chapter has been so designed that th

Maths Class X Question Bank Triangles Questions Bank-MCQ-Triangles - Class X Choose the Correct options Time limit: 0 Quiz Summary 0 of 34 Questions completed Questions: Information You have already completed the quiz before. Hence you can not start it again. Quiz is loading You must sign in or sign up to start the quiz. Questions Bank-MCQ-Triangles - Class X Read More Karnataka SSLC Class 10 Maths Solutions Chapter 2 Triangles Exercise 2.3. Question 1. State which pairs of triangles In the following figures are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: ∴ ∆ABC ~ ∆PQR Triangle ABC: Side Ab 3 cm Side Bc 2 cm Side Ca 5 cm Triangle DEF Side De 4.5 cm Side Ef x Side Fd 7.5 cm what is the legnth of side ef A 1.5 cm B 4 cm*** C 3 cm D 8.5 cm Am i correct? math Triangle ABC undergoes a series of transformations to result in triangle DEF

(a) Given, in two Δ ABC and Δ PQR, AB/QR = BC/PR = CA/PQ which shows that sides of one triangle are proportional to the side of the other triangle, then their corresponding angles are also equal, so by SSS similarity, triangles are similar DE EF DF = = Hence proved 4. Prove that if the areas of two similar triangles are equal then they are congruent. Sol: ∆ABC ∼ ∆PQR ( ) 2 2 2 ( ) ar ABC AB BC AC So ar PQR PQ QR PR ∆ = = = ∆ But ( ) 1 ( ) ar ABC ar PQR ∆ = ∆ (areas are equal) 2 2 2 1 AB BC AC PQ QR PR = = = Notice that when ∆ PQR ≅ ∆ ABC, then sides of ∆ PQR fall on corresponding equal sides of ∆ ABC and so is the case for the angles. That is, PQ covers AB, QR covers BC and RP covers CA; ∠ P covers ∠ A, ∠ Q covers ∠ B and ∠ R covers ∠ C. Also, there is a one-one correspondence between the vertices

Q5. In triangles ABC and DEF, B = E, F = C and AB = 3 DE. Then, the two triangles are (A) congruent but not similar (B) similar but not congruent (C) neither congruent nor similar (D) congruent as well as similar Q.6 The perimeters of two similar triangles ABC and PQR are respectively 36cm and 48cm. If PQ = 12cm, then AB = If in two right triangles, one of the acute angle of one triangle is equal to an acute If ∆A ~ ∆DEF, A = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆A . Perimeter of ∆PQR = 48 cm So, AB/PQ = AC/PR = BC/QR Then, perimeter of ∆A /perimeter of ∆PQR = A/PR 32/48 = AC/6 . ML Aggarwal Solutions for Class. 5.1 Congruence and Triangles 235 Use the two triangles at the right. a. Identify all corresponding congruent parts. b. Determine whether the triangles are congruent. If they are congruent, write a congruence statement. Solution a. Corresponding Angles Corresponding Sides aD ca G DE&**cGE&* aDEF ca GEF DF&**cGF&* aDFE ca GFE EF&*cEF&* b Click hereto get an answer to your question ️ In PQR, E and F are points on the sides PQ and PR respectively. verify EF || QR. PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm, FR = 2.4 cm In given figure PQR is a right triangle, right angled at Q and QS ⊥ PR. If PQ = 6 cm and PS = 4 cm, then find QS, RS and QR. asked Feb 12, 2018 in Class X Maths by akansha Expert ( 2.2k points

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of APQR should be equal to side BC of AABC so that the two triangles are congruent? Give reason for your answer. Solution: Question 3. If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles are the triangles that look the same but the sizes can be different. Similar triangles are different from congruent triangles. There are various methods by which we can find if two. In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE, then the two triangles are (a) congruent but not similar (b) similar but not congruent (c) neither congruent nor similar (d) congruent as well as similar. Answer 4. In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C AB = 3DE ∵ Two angles of the one triangles are equa RQ = 10 cm and BC = 6 cm. What is the length of PR? Which type of triangle is PQR? 20. In the figure ABC ~ PQR. What is the value of x? A 4 5 B C 6 R 6 7.2 P x Q 21. In PQR, DE || QR and 1. 4 DE QR Find ar. PQR ar PDE P D E Q R 22.In triangles ABC and PQR if B = Q and 1 2 AB BC PQ QR then what is the value of ? PR QR

(c) In figure (3) given below, ∠PQR = ∠PRS. Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ. Solution: Similarity Class 10 ICSE ML Aggarwal Solutions Question 11. In the given figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM × NP. Statement: Prove that, in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. To prove: ∠ABC = 90° Const.: Draw a right angle ∆DEF in which DE = BC and EF = AB. Proof: In rt. ∆ABC, AB 2 + BC 2 = AC 2 (i) Given In rt. ∆DEF DE 2 + EF 2. Draw another triangle PQR with PQ = 5 cm, QR = 6.5 cm and PR = 4 cm. Make a copy of triangle ABC on a tracing paper and try to make it cover triangle PQR with A on P, B on Q and C on R. Thus, AB = PQ; BC = QR and CA = RP. We observe that the two triangles cover each other exactly. So, triangle ABC ≅ triangle PQR EFDF DE EF (A) (B) PR PQ PQ RP DEDF EFDE (C) (D) QRPQ RP QR 7. In triangles ABC and DEF, B = E, F = C and AB = 3 DE. Then, the two triangles are (A) congruent but not similar (B) similar but not congruent (C) neither congruent nor similar (D) congruent as well as similar BC 1 ar (PRQ) 8 AB/DE = BC/EF = CA/FD = k, where k is the equivalent ratio or the trigonometric ratio. Corresponding Sides in Right Triangles If the lengths of the hypotenuse and a leg of one right-angled triangl e are proportional to the corresponding parts of the other right triangle, then the triangles are similar

- Considering the two triangles PQR and XYZ In ∆ PQR and XYZ PQ = XZ = 7 cms PR = YZ = 6 cms RQ = XY = 5 cms ∠PRQ = ∠XYZ ∠PQR = ∠XZY In the above 2 triangles 5 pairs of the congruent present. Still, they are not congruent. Question 9. If ∆ ABC and ∆ PQR are to be congruent, name one additional pair of corresponding parts
- 1. Which of the following pairs of triangles are congruent? In each case, state the condition of congruency: (a) In ΔABC and ΔDEF, AB = DE, BC = EF and B = E. (b) In ΔABC and ΔDEF, B = E = 90o; AC = DF and BC = EF. (c) In ΔABC and Δ QRP, AB = QR, B = R and C = P. (d) In ΔABC and Δ PQR, AB = PQ, AC = PR and BC = QR
- We know that, if two triangles are similar, then their corresponding angles are equal. ∴ ∠D = ∠R, ∠E = ∠P and ∠F =

Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ. Solution: Question 11. In the given figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM × NP = CN × MP. Solution: Question 12. Prove that the ratio of the perimeters of two similar triangles. **Triangle** **PQR** has vertices P(-2,8), Q(2,4), and R(4,6), which best describes **triangle** **PQR**? A- a right **triangle** with PQ ㅗ **QR** B- a right **triangle** with PQ ㅗ **PR** C- an isosceles **triangle** with PQ congruent to **QR** D- an isosceles **triangle** with PQ congruent with . Math. As part of a geometry assignment, John drew an equilateral **triangle**

If in triangles ABC and DEF,\(\frac { AB }{ DE } =\frac { BC }{ FD } \) , then they will be similar when (a) ∠B = ∠E (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠A = ∠F Solution: Question 9. If ∆PQR ~ ∆ABC, PQ = 6 cm, AB = 8 cm and perimeter of ∆ABC is 36 cm, then perimeter of ∆PQR is (a) 20.25 cm (b) 27 cm (c) 48 cm (d) 64 cm Solution. Here, PQ/XY = QR/YZ = PR/XZ. ∴ \(\triangle\)PQR∼ \(\triangle\)XYZ . iii) Side, Angle, Side similarity test. Fig: SAS . If two corresponding sides of two triangles are proportional and the angle contained by these sides are equal, then the triangles are similar

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