Questions: Which two triangles are congruent by the ASA Theorem? Complete the congruence statement. Δ □ △ □

Transcript text: Which two triangles are congruent by the ASA Theorem? Complete the congruence statement. $\Delta \square \triangle$ $\square$

Solution

Solution Steps

Step 1: Identify the ASA theorem

The ASA theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Step 2: Analyze the given triangles

We are given three triangles: ΔABC, ΔDEF, and ΔUVW. We need to find which two triangles have two congruent angles and a congruent included side.

ΔABC: ∠B, side BC, and ∠C are marked.
ΔDEF: ∠D, side DE, and ∠E are marked.
ΔUVW: ∠U, side UV, and ∠V are marked.

Step 3: Compare the triangles

Comparing ΔABC and ΔUVW, we see that:

∠B ≅ ∠U
BC ≅ UV
∠C ≅ ∠V

Thus, ΔABC ≅ ΔUVW by the ASA theorem.

Final Answer: ΔABC ≅ ΔUVW

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