CONGRUENT TRIANGLES WORKSHEET WITH ANSWER

Problem 1 :

Check whether two triangles PQR and WXY are congruent.

Problem 2 :

Check whether two triangles PQR and JKL are congruent. 

Problem 3 :

Check whether two triangles PQR and ABC are congruent.

Problem 4 :

Check whether two triangles PQR and CDE are congruent.

Problem 5 :

Check whether two triangles PQR and STU are congruent.

Problem 6 :

Check whether two triangles PQR and RST are congruent.

1. Answer :

(i) Triangle PQR and triangle WXY are right triangles. Because they both have a right angle. 

(i) PQ  =  XY (Hypotenuse). 

(ii) PR  =  WX (Leg)

Hence, the two triangles PQR and WXY are congruent by Hypotenuse-Leg theorem. 

2. Answer :

(i) PR  =  LK (Given)

(ii) ∠R  =  ∠K (Given)

(i) RQ  =  JK (Given)

Hence, the two triangles PQR and JKL are congruent by SAS postulate.

3. Answer :

(i) PQ  =  BC (Hypotenuse)

(ii) ∠Q  =  ∠B (Acute angle)

Hence, the two triangles PQR and ABC are congruent by Hypotenuse-Acute Angle theorem.

4. Answer :

(i) ∠R  =  ∠D (Given)

(ii) PR  =  ED (Given)

(iii) ∠P  =  ∠E (Given)

Hence, the two triangles PQR and CDE are congruent by ASA postulate. 

5. Answer :

(i) PQ  =  ST (Given)

(ii) PR  =  SU (Given)

(iii) QR  =  TU (Given)

Hence, the two triangles PQR and STU are congruent by SSS postulate. 

6. Answer :

(i) PR  =  RT (Given)

(ii) ∠SRT  =  ∠PRQ (Vertical Angles)

(iii) QR  =  RS (Given)

Hence, the two triangles PQR and RST are congruent by SAS postulate. 

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