Marcus and Marlee are comparing two right triangles to determine if they are congruent. Marcus has △ABC with a right angle at B . Side AB¯¯¯¯¯¯¯¯ has 2 tick marks, and the hypotenuse has 1 tick mark. Marlee has △PQR with a right angle at Q . Side QR¯¯¯¯¯¯¯¯ has 2 tick marks, and the hypotenuse has 1 tick mark. 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)

Question

Responses
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.
Neither is correct; the triangles are congruent by Side-Side-Angle.
Neither is correct; the triangles are congruent by Side-Angle-Side.
Marlee is correct; the triangles are not congruent because the corresponding legs are not marked as congruent.

Answer 1

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

Answer 2

If ΔABC≅CDA by the HL Theorem and AC¯¯¯¯¯¯¯¯=84 m and AD¯¯¯¯¯¯¯¯=85 m, how long is BA¯¯¯¯¯¯¯¯? (1 point) Responses 22 m 13 m 15 m 27 m

Answer 3

In order to find the length of BA¯¯¯¯¯¯¯¯, we need to use the information given and apply the HL Congruence Theorem.

According to the HL Congruence Theorem, if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Given that ΔABC≅CDA by the HL Theorem and AC¯¯¯¯¯¯¯¯=84 m and AD¯¯¯¯¯¯¯¯=85 m, we can conclude that side AB¯¯¯¯¯¯¯¯ and side CD¯¯¯¯¯¯¯¯ are congruent.

Therefore, the length of BA¯¯¯¯¯¯¯¯ is also 85 m, as it is congruent to CD¯¯¯¯¯¯¯¯.

So the correct answer is 85 m.