Question

marcus and marlee are comparing \\( \triangle a b c \\) with right angle \\( b \\) with \\( \triangle p q r \\) with right angle \\( q \\) to determine if they are congruent. \\( \overline{a b} \cong \overline{q r} \\) and \\( \overline{a c} \cong \overline{p r} \\). marcus says the triangles are congruent by the hl congruence theorem, but marlee does not agree. who is correct? (hint: draw a picture.) (1 point)
marcus is correct; the triangles are right triangles where a leg and the hypotenuse of one triangle is congruent to a leg and hypotenuse of the other triangle.
marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent.
neither is correct, the triangles are congruent by side-angle-side.
neither is correct; the triangles are congruent by side-side-angle

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 this case, for right - angled triangles \(\triangle ABC\) (\(\angle B = 90^{\circ}\)) and \(\triangle PQR\) (\(\angle Q=90^{\circ}\)), we are given \(\overline{AB}\cong\overline{QR}\) (a leg) and \(\overline{AC}\cong\overline{PR}\) (the hypotenuse).

Answer:

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