Question

consider the two triangles.
based on the two triangles’ markings, which statement is true?
○ the angle-angle-side congruency postulate proves the triangles are congruent.
○ the side-side-angle congruency postulate proves the triangles are congruent.
○ the side-angle-side congruency postulate proves the triangles are congruent.
○ the side-side-side congruency postulate proves the triangles are congruent.

Explanation:

Step1: Analyze the given information

We have two right - angled triangles. One angle (\(36.9^{\circ}\)) is given for each triangle, and one side (\(3\)) is given for each triangle.

Step2: Recall congruence postulates

• Angle - Angle - Side (AAS): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.
• Side - Side - Angle (SSA): Not a valid congruence postulate in general (except for right - angled triangles in some cases, but it's not a standard postulate like AAS, ASA, SAS, SSS).
• Side - Angle - Side (SAS): Requires two sides and the included angle. Here we don't have two sides and an included angle information.
• Side - Side - Side (SSS): Requires all three sides. Here we only know one side length.

For the two right - angled triangles, we know one right angle (common to both as they are right - angled), one other angle (\(36.9^{\circ}\)) and one non - included side (the side of length \(3\)).

Answer:

The Angle - Angle - Side congruency postulate proves the triangles are congruent.