Chapter 8.3, Problem 21PSC

To determine

To prove:Triangle ABC is similar to triangle GHI.

Explanation of Solution

Given information:

  $\begin{array}{l}\Delta ABC\sim \Delta DEF\\ \Delta DEF\sim \Delta GHI\end{array}$

Formula used:

The below properties are used:

Corresponding angles of similar triangles are congruent.

Transitive Property: If two segments (or angles) are each congruent to a third segment (or angle),then they are congruent to each other.

Proof:

  

It is given that,

  $\begin{array}{l}\Delta ABC\sim \Delta DEF\\ \Delta DEF\sim \Delta GHI\end{array}$

Corresponding angles of similar triangles are congruent.

  $\angle A \cong \angle D$

  $\angle D \cong \angle G$

By transitive property,we get

  $\angle A \cong \angle G$

Corresponding angles of similar triangles are congruent.

  $\angle B \cong \angle E$

  $\angle E \cong \angle H$

By transitive property, we get

  $\angle B \cong \angle H$

Two triangles are similar by AA similarity rule.

  $\Delta ABC\sim \Delta GHI$