Chapter 4.3, Problem 6CE

To determine

To find: The relation between sides $\overline{AP}\text{ and }\overline{BP}$ .

Answer to Problem 6CE

  $AP=BP$

Explanation of Solution

Given Information: In the figure shown, $M$ is the mid-point of $\overline{AB}$ and plane $X\perp \overline{AB}\text{ at}M$ .

  

Calculation:

Using two-column proof.

Statements	Reasons
$\overline{MP}=\overline{MP}$	Reflexive property
$\overline{AM}=\overline{MB}$	$M$ is the mid-point of $\overline{AB}$ . A midpoint divides a line segment into two equal parts.
$\angle AMP=\angle BMP$	Given
$\Delta AMP\cong \Delta BMP$	BY SAS Postulate
$\overline{AP}=\overline{BP}$	Using congruent parts of congruent triangles

Therefore, the answer is $AP=BP$ .