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 not congruent because of the corresponding legs are not marked congruent.

neither are correct; the triangles are congruent by side - angle - side.

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.

Explanation:

Step1: Recall HL Congruence Theorem

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.

Step2: Identify given information

We are given that $\triangle CAT$ with right angle $A$ and $\triangle DOG$ with right angle $O$, $\overline{CA}\cong\overline{DO}$ (a leg) and $\overline{CT}\cong\overline{DG}$ (the hypotenuse).

Step3: Apply HL Congruence Theorem

Since we have two right - triangles where a leg and the hypotenuse of one triangle are congruent to a leg and the hypotenuse of the other triangle, by the HL Congruence Theorem, the two triangles are congruent. So Matt is correct.

Answer:

D. 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.