Chapter 7.6, Problem 30STP

To determine

Find the information from the given option which is enough to prove that given similarity.

Answer to Problem 30STP

The right option is $H$ .

Explanation of Solution

Given:

The given diagram is

  

Prove that $\Delta LNQ\sim \Delta MPQ$ .

Calculation:

The right option is $H$ .

  $\overline{LN}$ and $\overline{PM}$ are parallel.

Proof

  

  $\overline{LN}$ and $\overline{PM}$ are parallel.

If two parallel lines $\left( \overline{LN}\text{ and }\overline{PM} \right)$ are cut by a transversal $\left( \overline{LM}\text{ or }\overline{NP} \right)$ , the alternate interior angles are congruent.

  $\begin{array}{l}\angle QPM\cong \angle QNL\\ \angle QMP\cong \angle QLN\end{array}$

When two lines are intersect each other form a pair of vertical angles. Vertical angles are equal to each other.

  $\angle PQM\cong \angle LQN$

By the use of $AAA$ similarity property.

  $\Delta LNQ\sim \Delta MPQ$ proved