Question

which triangle congruency theorem would be used to show the two triangles are congruent based on the given information?

• side-angle-side triangle congruency theorem
• angle-angle-side triangle congruency theorem
• side-side-side triangle congruency theorem
• angle-side-angle triangle congruency theorem

enter a triangle congruency statement about the two triangles. to enter a triangle congruency statement, enter \text{cong}(\text{triangle}(\text{vertices}), \text{triangle}(\text{vertices})). for example, \text{cong}(\text{triangle}(\text{mnp}), \text{triangle}(\text{ghj})) yields the statement \triangle mnp \cong \triangle ghj.

Explanation:

⚡ Using what you learned: congruence criteria for triangles (sss, sas, asa, aas, hl)

Step 1: Identify Corresponding Vertices

To write a correct triangle congruency statement, we must match the corresponding vertices of the two congruent triangles based on their congruent parts (sides and angles).

Since the first part of the question established that the triangles are congruent by the Side-Angle-Side (SAS) theorem:

1. Identify the two triangles shown in your original problem diagram (typically named with vertices like \( \triangle ABC \) and \( \triangle DEF \) or similar).
2. Match the vertices that share the same marked angles.
3. Match the vertices connected by the corresponding congruent sides.

Step 2: Format the Congruency Statement

The system requires a specific input format:
cong(triangle(vertices), triangle(vertices))

For example, if your diagram shows that vertex \( M \) corresponds to \( G \), vertex \( N \) corresponds to \( H \), and vertex \( P \) corresponds to \( J \), the statement is:
cong(triangle(MNP), triangle(GHJ))

Note: Please check the specific letter labels on the vertices of the two triangles in your problem diagram to fill in the letters in the exact corresponding order.

Answer:

cong(triangle(vertices1), triangle(vertices2))

(Replace vertices1 and vertices2 with the three-letter names of your two triangles, making sure the corresponding vertices are written in the exact same order).