Question

Triangle KMN is congruent to triangle PRT. Find the value of x.

Answer 1

Congruent triangles have congruent sides and angles. If ΔKMN≅ΔPRT (given) then from the diagram you can conclude that

• KM≅PR;
• MN≅RT;
• KN≅TP.

If MN≅RT, then

3x-1=20,

3x=20+1,

3x=21,

x=21:3,

x=7.

Answer: x=7.

Answer 2

We are given that

triangle KMN and triangle PRT are congruent

so, their corresponding sides must be equal

so, we can get

$KM=PR$

$MN=RT$

$NK=TP$

we are given

$KM=15$

$MN=20$

$NK=25$

$RT=3x-1$

now, we can plug this value

$MN=RT=3x-1$

$20=3x-1$

now, we can solve for x

Add 1 on both sides

$20+1=3x-1+1$

$21=3x$

Divide both sides by 3

and we get

$x=7$..............Answer