Question

1. In triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ. Also, AY = 7, BZ = 8, and XZ = 18. What is the perimeter of triangle ABC? (SHOW WORK)


2. What is y? (SHOW WORK) 2nd picture is the triangle.

Answer 1

Answer:

Part 1) The perimeter of triangle ABC is 24 units

Part 2) $y=97\°$

Step-by-step explanation:

Part 1)

we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

The perimeter of triangle ABC is equal to

$P=AB+BC+AC$

Applying the Midpoint Theorem

Find the measure of AB

$AB=\frac{XZ}{2}$

substitute given value

$AB=\frac{18}{2}=9\ units$

Find the measure of BC

$BC=\frac{XY}{2}$

$XY=2AY$

substitute given value

$XY=2(7)=14\ units$

$BC=\frac{14}{2}=7\ units$

Find the measure of AC

$AC=\frac{YZ}{2}$

$YZ=2BZ$

substitute given value

$YZ=2(8)=16\ units$

$AC=\frac{16}{2}=8\ units$

Find the perimeter  of triangle ABC

$P=9+7+8=24\ units$

Part 2)

step 1

Find the measure of angle z

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

$55\°+42\°+z=180\°\\97\°+z=180\°\\z=180\°-97\°\\z=83\°$

step 2

Find the measure of angle y

we know that

$y+z=180\°$ ----> by supplementary angles (form a linear pair)

substitute the value of z

$y+83\°=180\°$

$y=180\°-83\°=97\°$