Triangle Congruence Quiz

1. In the given congruent triangles under ASA, find the value of X, ΔPQR = ΔSTU. Congruence of Triangles Class 7 Extra Questions Maths Chapter 7

10

40

50

30

In congruent triangles under ASA, the angle-side-angle postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Since ΔPQR and ΔSTU are congruent, we can conclude that the measure of angle P is equal to the measure of angle S, the measure of angle Q is equal to the measure of angle T, and the measure of angle R is equal to the measure of angle U. Therefore, the value of X must be 30 degrees.

Explanation

In congruent triangles under ASA, the angle-side-angle postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Since ΔPQR and ΔSTU are congruent, we can conclude that the measure of angle P is equal to the measure of angle S, the measure of angle Q is equal to the measure of angle T, and the measure of angle R is equal to the measure of angle U. Therefore, the value of X must be 30 degrees.

2. In the given congruent triangles under ASA, find the value of Y, ΔPQR = ΔSTU.
Congruence of Triangles Class 7 Extra Questions Maths Chapter 7

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90

120

130

In congruent triangles, ASA (Angle-Side-Angle) is a condition where two triangles have one pair of corresponding angles equal and the included sides equal. In this case, since ΔPQR is congruent to ΔSTU under ASA, it means that angle P is equal to angle S, angle Q is equal to angle T, and the included side PR is equal to the included side ST. Therefore, the value of Y, which is the measure of angle Q, is equal to 90 degrees.

Explanation

In congruent triangles, ASA (Angle-Side-Angle) is a condition where two triangles have one pair of corresponding angles equal and the included sides equal. In this case, since ΔPQR is congruent to ΔSTU under ASA, it means that angle P is equal to angle S, angle Q is equal to angle T, and the included side PR is equal to the included side ST. Therefore, the value of Y, which is the measure of angle Q, is equal to 90 degrees.

3.

A

B

C

D

4. In the given figure, name the side opposite to vertex A. Congruence of Triangles Class 7 Extra Questions Maths Chapter 7

C

B

BC

ABC

In the given figure, the side opposite to vertex A is BC. This is because in a triangle, the side opposite to a vertex is the side that does not connect to that vertex. In this case, vertex A is connected to sides B and C, but not to side BC. Therefore, BC is the side opposite to vertex A.

Explanation

In the given figure, the side opposite to vertex A is BC. This is because in a triangle, the side opposite to a vertex is the side that does not connect to that vertex. In this case, vertex A is connected to sides B and C, but not to side BC. Therefore, BC is the side opposite to vertex A.

5.

A

B

C

D

.

Explanation

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6.

A

B

C

D

To determine congruence, we need to match corresponding sides and angles:

Side: KJ ≅ NP (both have a single hash mark)

Side: JL ≅ PM (both have double hash marks)

Angle: ∠KJL ≅ ∠NPM (both have the same angle marking)

Therefore, by Side-Angle-Side (SAS) congruence, ΔKJL ≅ ΔNPM

Explanation

To determine congruence, we need to match corresponding sides and angles:

Side: KJ ≅ NP (both have a single hash mark)

Side: JL ≅ PM (both have double hash marks)

Angle: ∠KJL ≅ ∠NPM (both have the same angle marking)

Therefore, by Side-Angle-Side (SAS) congruence, ΔKJL ≅ ΔNPM

7.

A

B

C

D

Explanation

8.

A

B

C

D

9.

A

B

C

D

10.

A

B

C

D