Download AdvGeo-Ch09-Test

1 of 6
Advanced Geometry - Chapter 9 Test
Name
Period
Date
__
Directions:
1.
Show all necessary work for the questions indicated with (W).
2.
Any unrelated writing, marks, or computation to the answer left will cause you loss of
3.
4.
5.
some points.
Reduce all fractions and radicals to simplest form.
Box or circle your answers.
Not all figures are drawn to scale.
1.
Complete each statement.
2.
(3 pts each blank)
(a)
The ________________ is the side opposite the right angle in a right triangle.
(b)
In an isosceles right triangle, if the hypotenuse has length 5√2, then each leg has length
________________.
(c)
In a right triangle, if r and s are the lengths of the legs and t is the length of the
hypotenuse, then ________________.
(d)
In a 30°-60°-90° triangle, if the shorter leg has length p, then the longer leg has length
________________ and the hypotenuse has length ________________.
Simplify the radical expression showing prime factorization process. (W)
(6 pts)
√108
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3.
Solve each problem below. All measurements in (a)-(c) are in centimeters.
(a)
m = __________ (W)
(6 pts)
(b)
Is ABC a right triangle? If not, is it acute or obtuse? (W)
(6 pts)
(c)
AB = __________ (W)
(6 pts)
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4.
Draw a right triangle whose hypotenuse is AB . Then find AB. (W)
(5 pts)
5.
Two jets pass directly over each other at 10 P.M. One jet is traveling south at 480 km/h; the
other is traveling east at 900 km/h. How far apart are the two jets at midnight? (6 pts)
6.
What is the length of the longer leg of a 30°-60°-90° triangle with a hypotenuse of length
24 3 m? (You must use the ratio of the side lengths.) (W)
(6 pts)
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7.
Find the x-coordinate of point P that is located in Quadrant II of the coordinate plane where
OP = 25. (W)
(6 pts)
P(x, 7)
25
O
8.
Find the perimeter of an equilateral triangle with its median measuring 9 m. (W)
(Do not change radicals to decimals.)
(6 pts)
9.
Determine whether ABC with vertices A(2, 4), B(10, 2), and C(7, 7) is scalene, isosceles,
or equilateral. (Do not change radicals to decimals.) (W)
(8 pts)
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10.
Find the circumference of a circle circumscribed about a square with perimeter 40 in.
(The square is inside touching the circle; Simplify radicals, not to decimals) (W) (6 pts)
11.
Find the measure of angle x, given segments 𝑚 ∥ 𝑛. (W)
(6 pts)
154°
m
x
40°
n
12.
Find the length of ̅̅̅̅
𝐴𝐵 . (You need to use ratios of special right triangles) (W)
(6 pts)
B
18cm
C
30°
45°
A
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13.
In parallelogram SQIT, 𝑚∠𝑄 = 2𝑥 + 5 and 𝑚∠𝑇 = 5𝑥 − 40. Find the measure of ∠𝑆.
(W)
(6 pts each)
Bonus problem:
14. Given the radius 5cm of circle O that circumscribes about a regular hexagon, find the area
of the regular hexagon. (W)
(5 pts)
E
I
F
5cm
O
H
D
G
Advanced Geometry