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:

It is given that

In ∆ ABC and ∆ DEF

AB = DE and AC = EF

The two angles from the two triangles which are equal so that the two triangles are congruent are ∠A = ∠E

From SAS criterion

The SAS criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are congruent.

∆ ABC ≅ ∆ EDF

Therefore, the two angles from the two triangles that must be equal so that the two triangles are congruent are ∠A and ∠E.

✦ Try This: In the two triangles PQR and XYZ, PQ = XY and PR = YZ. Name two angles from the two triangles that must be equal so that the two triangles are congruent. Give reason for your answer.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.2 Sample Problem 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

Summary:

In the two triangles ABC and DEF, AB = DE and AC = EF. The two angles from the two triangles that must be equal so that the two triangles are congruent is ∠A = ∠E. When ∠A = ∠E, ∆ ABC ≅ ∆ EDF from SAS criterion

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