# CONGRUENT TRIANGLES WORKSHEET WITH ANSWER

Congruent Triangles Worksheet with Answer :

Worksheet given in this section will be much useful for the students who would like to practice problems on proving triangle congruence.

Before look at the worksheet, if you would like to know the stuff related to triangle congruence and similarity,

## Congruent Triangles Worksheet with Answers - Problems

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.

## Triangle Congruence and Similarity Worksheet - Solutions

Problem 1 :

Check whether two triangles PQR and WXY are congruent.

Solution :

(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.

Problem 2 :

Check whether two triangles PQR and JKL are congruent.

Solution :

(i) PR  =  LK (Given)

(ii) ∠R  =  ∠K (Given)

(i) RQ  =  JK (Given)

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

Problem 3 :

Check whether two triangles PQR and ABC are congruent.

Solution :

(i) PQ  =  BC (Hypotenuse)

(ii) ∠Q  =  ∠B (Acute angle)

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

Problem 4 :

Check whether two triangles PQR and CDE are congruent.

Solution :

(i) ∠R  =  ∠D (Given)

(ii) PR  =  ED (Given)

(iii) ∠P  =  ∠E (Given)

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

Problem 5 :

Check whether two triangles PQR and STU are congruent.

Solution :

(i) PQ  =  ST (Given)

(ii) PR  =  SU (Given)

(iii) QR  =  TU (Given)

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

Problem 6 :

Check whether two triangles PQR and RST are congruent.

Solution :

(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.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems on triangle congruence.

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