3. Consider the following diagram. Find the values of m and n that prove the two triangles are congruent by the
HL Theorem.

To solve the problem we must know about HL theorem.

According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.

The value of m and n are 3 and 6, respectively.

Given to us

If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore,

the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.

Substitute the value of m,

Hence, the value of m and n are 3 and 6, respectively.

Learn more about HL theorem:

link

m = 3, n = 6

Step-by-step explanation:

The hypotenuse leg (HL) theorem states that two triangles are said to be similar if one leg and the hypotenuse of the triangles are congruent.

From the diagram, comparing the hypotenuse of the triangles;

4m + 1 = 13

4m = 13 - 1

     = 12

m =

   = 3

m = 3

Also, comparing the sides;

2m + n = 8m - 2n

substitute the value of m to have,

6 + n = 24 - 2n

collect like terms,

n + 2n = 24 - 6

3n = 18

n =

    = 6

n = 6

m = 3, n = 6

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