Question

matt and mary are comparing △cat with right angle a with △dog with right angle o to determine if they are congruent. $overline{ca}congoverline{do}$ and $overline{ct}congoverline{dg}$. matt says that the triangles are congruent by the hl congruence theorem, but mary does not agree. who is correct? (hint: draw a picture!) (1 point)

neither are correct; the triangles are congruent by side - side - angle.
matt is correct; the triangles are right triangles where the leg and the hypotenuse of one triangle is congruent to a leg and hypotenuse of the other triangle.
neither are correct; the triangles are congruent by side - angle - side.
matt is correct; the triangles are not congruent because of the corresponding legs are not marked congruent.

Explanation:

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. In \(\triangle CAT\) and \(\triangle DOG\), \(\overline{CA}\cong\overline{DO}\) (legs) and \(\overline{CT}\cong\overline{DG}\) (hypotenuses) and both are right - triangles. So Matt is correct.

Answer:

Matt is correct; the triangles are right triangles where the leg and the hypotenuse of one triangle is congruent to a leg and hypotenuse of the other triangle.