Question

Given:

1 = 4
2 = 3

Prove:
AB = CD

Which of the following triangle congruence theorems would be used in this proof?

A) SSS
B) ASA
C) AAS

GEOMETERY

Answer 1

Answer: (B) ASA.

Step-by-step explanation: As shown in the attached figure, ABE and CDF are two congruent triangles. We need to find which congruence rule they both are following.

Following are the three rules of cogruence of two triangles in geometry -

(i) SSS rule - Here, all the three sides of one triangle are equal to the corresponding sides of the second triangle.

(ii) ASA rule - Here, two angles of one triangle are equal to the corresponding angles of the second and also the sides between them are equal.

(iii) SAS rule - Here, two sides of one triangle are equal to the corresponding two sides of the second triangle and the angles between the two sides of both the triangles are equal.

Since, in ΔABE and ΔCDF

∠1=∠4,

∠2=∠3

and

AB=CD.

So, here we are considering two angles and the side between them in both the triangles, so we are following ASA rule of congruence.

Thus, the correct option is (B) ASA.