Question

question
prove $\angle i \cong \angle w$ by filling out the flowchart below.

for each box, choose a statement format 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

$\angle WXV$ and $\angle JHI$ are right angles (given by the right angle symbols in the diagram), so $\angle WXV \cong \angle JHI$ (all right angles are congruent).

Step2: Identify Congruent Sides

From the diagram, $VX \cong JH$ (marked with two congruent segments) and $WV \cong JI$ (marked with one congruent segment).

Step3: Apply Hypotenuse - Leg (HL) Theorem

In right triangles $\triangle WXV$ and $\triangle JHI$, we have:

• Hypotenuse: $WV \cong JI$ (from Step 2)
• Leg: $VX \cong JH$ (from Step 2)
• Right angle: $\angle WXV \cong \angle JHI$ (from Step 1)

By the Hypotenuse - Leg (HL) Congruence Theorem, $\triangle WXV \cong \triangle JHI$.

Step4: Corresponding Parts of Congruent Triangles

Since $\triangle WXV \cong \triangle JHI$, their corresponding angles $\angle I$ and $\angle W$ are congruent (Corresponding Parts of Congruent Triangles are Congruent, CPCTC).

Answer:

To prove $\angle I \cong \angle W$, we follow these steps in the flowchart:

1. Statement: $\angle WXV \cong \angle JHI$

Reason: All right angles are congruent (given the right angle symbols in the diagram).

1. Statement: $VX \cong JH$ and $WV \cong JI$

Reason: Marked congruent segments in the diagram.

1. Statement: $\triangle WXV \cong \triangle JHI$

Reason: Hypotenuse - Leg (HL) Congruence Theorem (right triangles with congruent hypotenuse and leg).

1. Statement: $\angle I \cong \angle W$

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