Question

Which scenario is a counterexample that disproves the AAA criteria for congruence?

Two 45°−45°−90° triangles that share a diagonal to form a square

Two 45 degrees minus 45 degrees minus 90 degrees triangles that share a diagonal to form a square


Two right triangles with hypotenuses that are 6 in and 8 in

Two right triangles with hypotenuses that are 6 in and 8 in


Two isosceles triangles with bases of 2 ft and 7 ft

Two isosceles triangles with bases of 2 ft and 7 ft


Two equilateral triangles with side lengths of 4 cm and 10 cm

Answer 1

The scenario that disproves the AAA criteria for congruence is two right triangles with different hypotenuse lengths.

Step-by-step explanation:

The scenario that is a counterexample that disproves the AAA criteria for congruence is two right triangles with hypotenuses that are 6 in and 8 in.

The AAA (Angle-Angle-Angle) criteria for congruence states that if two triangles have the same angles, then they are congruent. However, in this scenario, the two right triangles have the same angles (since the two triangles are both right triangles) but different side lengths, specifically different hypotenuse lengths.

Therefore, the AAA criteria for congruence is disproven in this scenario, showing that having the same angles is not sufficient to guarantee triangle congruence.

Learn more about AAA criteria for congruence