Question

Given:

AB=CD
<1=<4
Prove:
AD=CB
Which of the following triangle congruence theroms would be used in this proof?
SSS
SAS
ASA

Answer 1

Answer and Step-by-step explanation:

We know that AB = CD and that angle 1 = angle 4. So, we have two corresponding sides congruent and two corresponding angles congruent.

We see that triangles ADC and ABC also share the side AC, so clearly

AC = AC. Now, this is our second pair of corresponding congruent sides.

Then, by SAS congruence theorem, we know that triangle ADC is congruent to triangle ABC. Since they are congruent, their corresponding sides will be equal. AD of triangle ADC corresponds to CB of triangle ABC. Thus, they are equal and AD = CB.

Hope this helps!

Answer 2

SAS

Explanation:

Since angle 1 = angle 4,

Segments AB and DC are parallel (alternate angles)

Triangles DCA and BAC have 2 sides equal (AB = CD and AC) and one congruent angle in between these sides.

Hence, the two triangles are congruent by SAS

Therefore, AD = CB