Question

Write a two-column proof.

Answer 1

Proof:-

In ∆XYZ and ∆VWZ

$\because\sf\begin{cases}\sf XZ\cong VZ(Given)\\ \sf YZ\cong WZ(Given)\\ \sf$

Hence

∆XYZ$\cong$∆VWZ(Side-Angle-Side)

Answer 2

Given:-

$\begin{gathered}\\ \sf\longmapsto XZ≅VZ\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto YZ≅WZ\end{gathered}$

To prove:-

⇒△ XYZ≅△ VWZ

Proof:-

In △ XYZ&△ VWZ we have,

• XZ=VZ [Given]
• ∠XZY=∠VZW [Vertically opposite angles]
• YZ=WZ [Given]

△ XYZ≅△ VWZ

Hence, Proved by side-angle-side theorem.