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=(1)/(2)AB \\ BD=AC,BD\parallel AC \end{gathered}`

To explain why △ABC is congruent to △DCB.

Step-by-step explanation:

It is given that,

d

`\begin{gathered} WQ=(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.