Chapter 8.4, Problem 4PSA

To determine

To show that two ratio are equal.

Answer to Problem 4PSA

  $JM/MKisequaltoHJ/JK.$

Explanation of Solution

Given information:

  $\begin{array}{l}\angle HJKisarightangle.\\ \overline{JM}isanaltitude.\end{array}$

Formula used:

The below properties are used:

An altitude forms perpendicular lines with sides.

Perpendicular lines form right angles.

Right angles are congruent.

Corresponding sides of similar triangles are proportional.

Proof:

  

It is given that,

  $\begin{array}{l}\angle HJKisarightangle.\\ \overline{JM}isanaltitude.\end{array}$

An altitude forms perpendicular lines with sides.

  $\overline{JM}\perp \overline{HK}$

Perpendicular lines form right angles.

  $\angle JMKisarightangle.$

Right angles are congruent.

  $\angle JMK\cong \angle HJK$

By reflexive property, we get

  $\angle K\cong \angle K$

By AA similarity rule, we get

  $\Delta JMK~ \Delta HJK$

Corresponding sides of similar triangles are proportional.

  $JM/MK=HJ/JK$