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bagirrra123 [75]
3 years ago
13

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.

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
6 0

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 <u><em>Midpoint Theorem</em></u> 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

see the attached figure to better understand the problem

so

Applying the midpoint theorem

step 1

Find the value of BC

BC=\frac{1}{2}XY

XY=2AY ---> because A is the midpoint

substitute the given value of AY

XY=2(7)=14\ units

BC=\frac{1}{2}(14)=7\ units

step 2

Find the value of AC

AC=\frac{1}{2}YZ

YZ=2BZ ---> because B is the midpoint

substitute the given value of BZ

YZ=2(8)=16\ units

AC=\frac{1}{2}(16)=8\ units

step 3

Find the value of AB

AB=\frac{1}{2}XZ

substitute the given value of XZ

AB=\frac{1}{2}(18)=9\ units

step 4

Find the perimeter of triangle ABC

P=AB+BC+AC

substitute

P=9+7+8=24\ units

Part 2) Find the measure of angle y

step 1

Find the measure of angle z

we know that

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

so

55\°+42\°+z=180\°

solve for z

97\°+z=180\°

z=180\°-97\°

z=83\°

step 2

Find the measure of angle y

we know that

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

we have

z=83\°

substitute

83\°+y=180\°

solve for y

y=180\°-83\°

y=97\°

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