Question

what are the corresponding parts of the figures below? select all that apply.
(figures of two triangles, one labeled with vertices i, g, h and angles 44°, 60°, 76° and side lengths 21 cm, 15 cm, 19 cm; the other labeled with vertices w, v, u and angles 60°, 76°, 44° and side lengths 15 cm, 21 cm, 19 cm)
options: ∠g ≅ ∠w, overline{ih} ≅ overline{uv}, overline{gi} ≅ overline{wu}, overline{hg} ≅ overline{vw}

Explanation:

Step1: Analyze Angles

Check angle measures: \( \angle G = 60^\circ \), \( \angle W = 60^\circ \), so \( \angle G \cong \angle W \).

Step2: Analyze Sides (Lengths)

• \( IH = 19 \, \text{cm} \), \( UV = 19 \, \text{cm} \) → \( \overline{IH} \cong \overline{UV} \).
• \( GI = 21 \, \text{cm} \), \( WU = 21 \, \text{cm} \) → \( \overline{GI} \cong \overline{WU} \).
• \( HG = 15 \, \text{cm} \), \( VW = 15 \, \text{cm} \) → \( \overline{HG} \cong \overline{VW} \).

All marked correspondences match angle/side congruence.

Answer:

\( \angle G \cong \angle W \), \( \overline{IH} \cong \overline{UV} \), \( \overline{GI} \cong \overline{WU} \), \( \overline{HG} \cong \overline{VW} \) (all selected options are correct as they match congruent angles/sides).