Question

In this diagram WQ = AB. One way to prove this is true is to draw a line through B such that BDAC. Then prove △ABC is congruent to △DCB, and use corresponding parts of the two triangles. Explain why △ABC is congruent to △DCB.

Answer 1

Given

$\begin{gathered} WQ=\frac{1}{2}AB \\ BD=AC,BD\parallel AC \end{gathered}$

To explain why △ABC is congruent to △DCB.

Explanation:

It is given that,

d

$\begin{gathered} WQ=\frac{1}{2}AB \\ BD=AC,BD\parallel AC \end{gathered}$

Since

$BD\parallel AC$

Then,

$\angle ACB=\angle DBC$

Also,

$\begin{gathered} BD=AC, \\ BC\text{ is common.} \end{gathered}$

Hence, by SAS ongruence rule △ABC is congruent to △DCB.