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

3 Consider The Following Diagram Find The Values Of M And N That Prove The Two Triangles Are Congruent By The HL Theorem class=

Sagot :

olayemiolakunle65

Answer:

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 = [tex]\frac{12}{4}[/tex]

   = 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 = [tex]\frac{18}{3}[/tex]

    = 6

n = 6

m = 3, n = 6

To solve the problem we must know about HL theorem.

What is the 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

  • The hypotenuse of the first triangle = 13
  • One leg of the first triangle = 2m+n
  • The hypotenuse of the second triangle = 4m+1
  • One leg of the second triangle = 8m - 2n

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.

Hypotenuse Congruent

[tex]4m + 1 =13\\\\4m=13-1\\\\m=\dfrac{12}{4}\\\\m=3[/tex]

Corresponding Congruent sides

[tex]2m+n = 8m-2n\\[/tex]

Substitute the value of m,

[tex]2(3)+n = 8(3)-2n\\\\6+n = 24-2n\\\\6-24 = -2n-n\\\\-18 = -3n\\\\n=\dfrac{-18}{-3}\\\\n = 6[/tex]

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

Learn more about HL theorem:

https://brainly.com/question/11804042

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