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: SAS congruence postulate

Step-by-step 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.

LL

Step-by-step 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°.)