Question

prove $\angle j \cong \angle v$ by filling out the flowchart below. for each box, choose a statement from the dropdown menu. you will then be able to change the letters to match the diagram for this problem.

Explanation:

Step1: Identify right angles

$\angle H = 90^\circ$, $\angle X = 90^\circ$ (Given right triangles)
$\angle H \cong \angle X$ (All right angles are congruent)

Step2: Mark congruent sides

$\overline{JH} \cong \overline{WV}$, $\overline{JI} \cong \overline{WV}$ (Given congruent side markings)

Step3: Prove triangle congruence

$\triangle JHI \cong \triangle VXW$ (HL Congruence Theorem: right triangles with congruent hypotenuse and leg are congruent)

Step4: Corresponding angles congruent

$\angle J \cong \angle V$ (CPCTC: Corresponding Parts of Congruent Triangles are Congruent)

Answer:

The completed flowchart statements and reasons are:

1. Type of Statement: $\boldsymbol{\angle H \cong \angle X}$

Reason: All right angles are congruent

1. Type of Statement: $\boldsymbol{\overline{JH} \cong \overline{WV}, \overline{JI} \cong \overline{WX}}$

Reason: Given (from diagram markings)

1. Type of Statement: $\boldsymbol{\triangle JHI \cong \triangle VXW}$

Reason: HL Congruence Theorem

1. Type of Statement: $\boldsymbol{\angle J \cong \angle V}$

Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)