Chapter 14.4, Problem 1MRE

To determine

To find: Triangles similar to $\Delta OBC$ .

Answer to Problem 1MRE

  $\Delta OBC$ is similar to $\Delta OFG$ & $\Delta ODE$ .

Explanation of Solution

Given information :

  $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

Concept used:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of thelengthsof their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides.

As per the given problem

Following diagram is provided.

  

Given: $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

In $\Delta OBC$ & $\Delta OFG$

  $\angle COB=\angle GOF$ (Common angle)

  $\angle OBC=\angle OFG$ ( $\overline{BC}\left|\right|\overline{FG}$ ) (corresponding angles)

  $\angle OCB=\angle OGF$ ( $\overline{BC}\left|\right|\overline{FG}$ ) (corresponding angles)

Therefore, $\Delta OBC$ similar to $\Delta OFG$ .

In $\Delta OBC$ & $\Delta ODE$

  $\angle COB=\angle DOE$ (Opposite angle)

  $\angle OBC=\angle ODE$ ( $\overline{BC}\left|\right|\overline{ED}$ ) (transverse angles)

  $\angle OCB=\angle OED$ ( $\overline{BC}\left|\right|\overline{ED}$ ) (transverse angles)

Therefore, $\Delta OBC$ similar to $\Delta ODE$ .

Hence,

  $\Delta OBC$ is similar to $\Delta OFG$ & $\Delta ODE$ .