Question

3 fill in the blank 4 points
use the image above to complete the cpctc proof homework matching.

• ( x y perp y w, q p perp z p, y w cong z p, x w cong q z )
• ( angle y ) and ( angle p ) are right angles
• ( \triangle x y w cong \triangle q p z )
• ( x y cong q p )

Explanation:

1. The first statement lists given conditions directly provided in the problem.
2. Perpendicular lines form right angles, so this follows the definition of perpendicular.
3. Two right triangles with congruent hypotenuses ($XW \cong QZ$) and one leg ($YW \cong ZP$) are congruent by HL (Hypotenuse-Leg) theorem.
4. Corresponding parts of congruent triangles are congruent (CPCTC), so $XY \cong QP$ is a result of triangle congruence.

Answer:

• $XY \perp YW, QP \perp ZP, YW \cong ZP, XW \cong QZ$: Given
• $\angle Y$ and $\angle P$ are right angles: Definition of Perpendicular
• $\triangle XYW \cong \triangle QPZ$: HL
• $XY \cong QP$: CPCTC