Exercise 80 Page 659

Consider the given triangle.

We are asked to find the values of x and y. We will do it one at a time.

Finding x

Since we are given a triangle with a line which is a midsegment of the triangle, we can use the Triangle Midsegment Theorem.

We can use the above theorem to write an equation that can be solved for x. x+2=1/2(3/2x+11) Let's solve it!

x+2=1/2(3/2x+11)

MultEqn

LHS * 2=RHS* 2

2(x+2)=3/2x+11

MultEqn

LHS * 2=RHS* 2

4(x+2)=2(3/2x+11)

Distr

Distribute 4 & 2

4x+8=3x+22

▼

Solve for x

SubEqn

LHS-3x=RHS-3x

x+8=22

SubEqn

LHS-8=RHS-8

x=14

Finding y

Now we will find the value of y. Let's take a look at the diagram.

We can see that the segments with measures 3y-9 and 2y+6 are congruent. Therefore, their measures are equal. 3y-9=2y+6 Let's solve the above equation for y.

3y-9=2y+6

▼

Solve for y

SubEqn

LHS-2y=RHS-2y

y-9=6

AddEqn

LHS+9=RHS+9

y=15