Question

1. given: ∠w and ∠y are right angles; \\( \overline { v x } \cong \overline { z x } \\); x is the midpoint of \\( \overline { w y } \\) prove: \\( \delta v w x \cong \delta z y x \\)

Explanation:

Step1: State given information

Given

Step2: Identify right triangles

\(\triangle VWX\) and \(\triangle ZYX\) are right triangles

Step3: State given information

Given

Step4: Identify equal segments

\(\overline{WX}\cong\overline{YX}\)

Step5: Prove triangles congruent

\(\triangle VWX\cong\triangle ZYX\) (by HL - Hypotenuse - Leg Congruence Theorem)

Answer:

1. Given
2. \(\triangle VWX\) and \(\triangle ZYX\) are right triangles
3. Given
4. \(\overline{WX}\cong\overline{YX}\)
5. \(\triangle VWX\cong\triangle ZYX\) (by HL - Hypotenuse - Leg Congruence Theorem)