Name: ____________________ Chapter 9 Study Guide – Sections 1 – 3: Solve for x. Then state whether or not the side lengths form a Pythagorean Triple. Keep your answers in EXACT, SIMPLEST FORM (No Rounding). 1.
2. 12 X
20
19 x 14
36
3.
13
4. x 39
x
6
Find the area of the following isosceles triangles. Round your answer to the nearest HUNDREDTH. 5.
6.
7.
19 25
25.4
25
13
h
25.4 18
7
1
Verify that the following segments form a triangle. Then, determine if it is acute, right, or obtuse. Rules: If the two smaller sides add to MORE than the biggest side, then it creates a triangle. If a2+b2=c2, then _________. If a2+b2c2, then ____________.
8. 10, 11, 14
9. 12, 16, 20
10. 15, 20, 36
11. 4.1, 8.2, 12.2
12. 24, 30, 6√43
13. 10, 15, 5√13
Use special right triangles to find each side length. 5 Steps in finding side lengths of special right triangles… 1) 2) 3) 4) 5)
14.
15.
16.
X
Y
2
17.
20.
23.
18.
19.
21.
22.
24.
25
3
Find the geometric mean of the two given numbers. Keep your answer in EXACT, SIMPLEST FORM. Definition of geometric mean:
𝑎 𝑥
=
𝑥 𝑏
, where x is the ____________________, and a and b are the two
numbers in which you are finding the geometric mean. 26.
8 and 28
27. 9 and 16
28. 24 and 45
Solve for x. 29. 6 is the geometric mean of x and 14.
30. 20 is the geometric mean of 16 and x.
Write a similarity statement for the THREE similar triangles. Then solve for x.