Question

prove $angle k cong angle w$ 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: List given congruent sides/angles

1. $\angle I \cong \angle Y$ (both are right angles, $90^\circ$)
2. $\overline{IK} \cong \overline{YW}$ (marked congruent segments)
3. $\overline{KJ} \cong \overline{XW}$ (marked congruent hypotenuses)

Step2: Apply HL congruence

For right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, the triangles are congruent. So $\triangle IKJ \cong \triangle YWH$ by HL.

Step3: Corresponding parts of congruent triangles are congruent

If $\triangle IKJ \cong \triangle YXW$, then all corresponding angles are congruent, so $\angle K \cong \angle W$.

Answer:

1. Top Left Box:

• Statement: $\angle I \cong \angle Y$
• Reason: Given (Right Angles)

1. Top Middle Box:

• Statement: $\overline{IJ} \cong \overline{XY}$
• Reason: Given

1. Top Right Box:

• Statement: $\overline{KJ} \cong \overline{XW}$
• Reason: Given

1. Bottom Box:

• Statement: $\triangle IKJ \cong \triangle YXW$
• Reason: HL (Hypotenuse-Leg Congruence)

1. Final Conclusion: $\angle K \cong \angle W$ (Corresponding Parts of Congruent Triangles are Congruent)