PSAT Math : Plane Geometry
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Example Questions
Example Question #1 : Right Triangles
Which angle or angles must be complementary to 
I)
II)
III)
IV)
V)
II only
I only
II and V only
I and III only
IV only
II and V only
Since 
The correct response is II and V only.
Example Question #1 : How To Find If Right Triangles Are Similar
Refer to the above figure. Given that 
By the Pythagorean Theorem,
The similarity ratio of 
which is subsequently the ratio of the perimeter of 
The perimeter of 
so the perimeter of 
Example Question #2 : How To Find If Right Triangles Are Similar
Note: Figure NOT drawn to scale.
Refer to the above figure. Given that
The correct answer is not among the other responses.
By the Pythagorean Theorem,
The similarity ratio of 
This can be used to find 
The area of 
Example Question #2 : How To Find If Right Triangles Are Similar
Note: Figures NOT drawn to scale.
Refer to the above figure. Given that 
By the Pythagorean Theorem, since 
The similarity ratio of 
Likewise,
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
A right triangle has one side equal to 5 and its hypotenuse equal to 14. Its third side is equal to:
14.87
12
9
13.07
171
13.07
The Pythagorean Theorem gives us a2 + b2 = c2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b2 = 142 – 52 = 171. Therefore b is equal to the square root of 171 or approximately 13.07.
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Which of the following could NOT be the lengths of the sides of a right triangle?
5, 12, 13
12, 16, 20
8, 15, 17
5, 7, 10
14, 48, 50
5, 7, 10
We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.
All of the other answer choices observe the theorem a2 + b2 = c2
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Which set of sides could make a right triangle?
6, 7, 8
4, 6, 9
9, 12, 15
10, 12, 16
9, 12, 15
By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.
Example Question #11 : How To Find The Length Of The Side Of A Right Triangle
A right triangle with a base of 12 and hypotenuse of 15 is shown below. Find x.
4
3.5
5
4.5
5.5
4
Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗2 –〖12〗2) = 9, so x=9 – 5=4
Example Question #131 : Plane Geometry
A right triangle has sides of 36 and 39(hypotenuse). Find the length of the third side
42
12 √6
33√2
15
33
15
use the pythagorean theorem:
a2 + b2 = c2 ; a and b are sides, c is the hypotenuse
a2 + 1296 = 1521
a2 = 225
a = 15
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?
4 hours and 0 minutes
3 minutes and 20 seconds
3 minutes and 50 seconds
2 hours and 30 minutes
1 hour and 45 minutes
3 minutes and 20 seconds
Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.
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