In a triangle xyz, ab is a midsegment. find the length of ab.

a. 25
b. 31
c. 30
d. 35

Option A.

Step-by-step explanation:

step 1

Find the value of x

we know that

If AB is a mid-segment, then AB is parallel to YZ

so

Triangles AXB and YXZ are similar by AA Similarity Theorem

Remember  that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

we have that

----> by Midpoint Theorem

substitute the given values in the expression above

solve for x

Multiply by (2x+2) both sides

Group terms

step 2

Find the length of AB

substitute the value of x

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: