Question

Triangles ABC and DBC have the following characteristics:

BC is a side of both triangles

∠ACB and ∠DCB are right angles

AC ≅ DC

Which congruence theorem can be used to prove △ABC ≅ △DBC?

Answer 1

Answer: SAS congruence postulate

Explanation:

Given : Triangles ABC and DBC have the following characteristics:

BC is a side of both triangles

∠ACB and ∠DCB are right angles

AC ≅ DC

Using the given information , we have made the following diagram.

Now, in ΔABC and ΔDBC

BC= BC [By Reflexive property]

∠ACB and ∠DCB= 90° [Measure of right angle = 90°]

AC ≅ DC [Given ]

So by SAS congruence postulate , we have

ΔABC ≅ ΔDBC

• SAS congruence postulate : if two sides and their included angle of a triangle are congruent to two sides and their included angle of second triangle then the two triangles are said to be congruent.

Answer 2

LL

Explanation:

You are given two congruent legs: BC≅BC and AC≅DC. The fact that it is a right triangle lets you invoke the LL theorem of congruence for right triangles. (This is a special case of the SAS theorem, where the A is 90°.)