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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?

Respuesta :

sqdancefan

Answer:

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°.)

JeanaShupp

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.
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