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)
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.
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.
To determine who is correct, we need to analyze the information given.
Marcus claims that the triangles are congruent using the HL Congruence Theorem. In the HL Congruence Theorem, two right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the corresponding hypotenuse and leg of the other triangle.
Marlee disagrees with Marcus, suggesting that the triangles are not congruent because the corresponding legs are not marked as congruent.
To determine who is correct, we need to examine the information provided.
Marcus has triangle ABC with a right angle at B. Side AB has 2 tick marks, and the hypotenuse has 1 tick mark.
Marlee has triangle PQR with a right angle at Q. Side QR has 2 tick marks, and the hypotenuse has 1 tick mark.
Based on the given information, Marcus is correct. The triangles are right triangles where a leg and the hypotenuse of one triangle are congruent to a leg and the hypotenuse of the other triangle. Therefore, the triangles are congruent by the HL Congruence Theorem.
To determine if Marcus or Marlee is correct, we first need to understand the HL Congruence Theorem. The HL Congruence Theorem states that 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.
Let's analyze the given information. Marcus has a right triangle △ABC, with a right angle at B. Side AB has 2 tick marks, and the hypotenuse has 1 tick mark. Marlee has a right triangle △PQR, with a right angle at Q. Side QR has 2 tick marks, and the hypotenuse has 1 tick mark.
To compare the triangles, we need to check if the hypotenuse and one leg of Marcus's triangle are congruent to the hypotenuse and one leg of Marlee's triangle. From the given information, we can see that both triangles have a hypotenuse with 1 tick mark, so that criterion is met.
Now let's compare the legs. Marcus's triangle has leg AB with 2 tick marks, while Marlee's triangle has leg QR with 2 tick marks. The legs are marked as congruent in both triangles.
Therefore, both the hypotenuse and one leg of Marcus's triangle are congruent to the hypotenuse and one leg of Marlee's triangle. According to the HL Congruence Theorem, the triangles are congruent.
Hence, Marcus is correct; the triangles are congruent by the HL Congruence Theorem.
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
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.