Question

Given: XZ bisects ZYXW
and ZYZW
Prove: AXYZ 2 AXWZ

Answer 1

Explanation:

Top Problem:

Reason:

1. Given

2. Definition of segment bisector ( segment bisector is a line, ray or segment that divides a segment into to congruent segments)

3. Vertical angles are congruent

4. SAS (Side ZP≅XP Angle ZPY ≅ WPX Side WP≅YP)

Bottom Problem

Reason:

1. Given

2. Definition of angle bisector ( an angle bisector is a line, ray or line segment that divides an angle in two congruent angles)

3. Definition of angle bisector

4. Reflexive Property ( a line segment is congruent with itself)

5. ASA (Angle Side Angle Theorem of Congruency)