REVIEW

Review Similarity and Right Triangles/Pythagorean Thm Name_____________________________#____Pd____
1.) Below polygons are similar. Determine value of x
2.) Rectangles are similar. Determine both perimeters.
12
3.) Given similar polygons 𝑅𝑇𝑌𝑈~𝐹𝐺𝐻𝐽, then ∡𝑇 ≅ _________
Solve for x.
4.
24
4
Show all work.
3
=𝑥
5.
𝑘−8
3
=
𝑘+2
4. x =_______
5
5. k = _______
6. Find the geometric mean of 6 and 30. Simplify any radicals in your answer.
Show answer in simplified radical form, no decimals.
7. The angles of a triangle are in the extended ratio of 1:5:6.
Find the measures of the 3 interior angles of the triangle.
6. _______
7. ______, ______,_______
Complete the statement and write which property you used.
8. If
x ?
x y
 , then  .
3 8
y ?
9. If
14 x
17 ?
 , then
 .
3 ?
3 y
8. _______
9. _______
10. Given ∆ABC ~ ∆DEF, which statement is not correct?
A.
BC BC

EF EF
B.
𝐴𝐵
𝐷𝐸
=
𝐵𝐶
𝐸𝐹
C.
AB CA

DE FD
Given the 3 segment lengths.
Determine if they form a right, acute or obtuse Δ.
6, 8, and 10.
The given lengths are two sides of a right triangle. All three
sides lengths of the triangle are integers. Determine the length
of the third side and tell whether it is a leg or hypotenuse.
80 and 89
10. _______
D.
CA BC

FD DE
Determine the Area of the triangle with the
given side lengths. 20cm, 32cm, and 20cm
Determine whether the following triangles are similar, circle yes or no. If yes, state the postulate or theorem that
makes them similar. Complete the similarity statement for the similar triangles. Triangles are not drawn to scale.
Do not forget notation, you will lose points.
11.
12.
13.
69˚
69˚
Yes
No
Yes
No
Yes
No
∆BCA ~ ________
∆BDC ~ ________
∆RST ~ ________
Reason: ___________
Reason: __________
Reason: __________
14. The perimeter of ∆PQR is 144, PQ = 30, ∆PQR ~ ∆STU, and ST = 25.
What is the perimeter of ∆STU? (HINT: draw and label the two triangles)
15. If p // q, solve for x.
14. _______
16. Solve for x.
15. x = ______
16.x=________
17. Solve for x.
18. Determine the geometric mean of the
following two numbers. 6 and 15
17. x =______
18. _______
19.) The perimeter of a rectangle is 120 inches. The ratio of the length to the width is 11:4.
Determine the area of the rectangle.
20.) Find x that makes KM // JN .
L
21.) Find the value of x, y, and z.
20. x =______
21. x=_______
8
K
12
y=________
5
J
z=_______
M
x
N