Memorize
Know your Vocabulary
List the first 15 perfect squares
Label the parts of these right triangles with the
1
words leg and hypotenuse.
4
9
16
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See the Story
Pythagorean Property of Right Triangles
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The square built on side a has 9 unites
The square built on side b has 16 units
The square built on side c has 25 units
Using this 3, 4, 5 triangle we can draw a picture of the Pythagorean Theorem.
1
The Greek mathematician Pythagoras, after much
experimenting with right triangles, made a very important
discovery. He drew squares on each of the three sides of a
right triangle and discovered that two of these
squares added together equal the third.
32 = 9
42 = 16
52 = 25
9 + 16 = 25
Determine the areas of the squares you could build on each leg of this right triangle. Use these
areas to find the length of the hypotenuse.
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2
Determine the areas of the squares you could build on the leg and hypotenuse of this right
triangle. Use these areas to find the length of the unlabeled leg.
Using the Pythagorean Theorem to compute the measurement of each hypotenuse. Show all
work on another sheet of paper for this section!!!!
1.
2.
3.
4.
Base
15in.
32 ft.
30 yd.
6 in.
Altitude
20 in.
24 ft.
40 yd.
8 in.
Hypotenuse
5.
6.
7.
8.
Base
36 mm.
9 cm.
80 in.
21 in.
Altitude
27 mm.
12 cm.
60 in.
28 in.
Hypotenuse
Example of using inverse operations to find a leg length.
h 2 = l2 + l 2
172 = 82 + b2
289= 64 + b2
-64 -64
225=b2
±√225 = 𝑏 2
b = +/- 15
The side length is 15 units.
A wire cable is attached to the top of a vertical pole that is 4 meters high. How long
must the cable be if it is fastened 3 meters from the base of the pole?
2.
A ladder reaches to the top of a sign 8 feet from the ground. How long is the ladder
from the bottom if it is placed 6 feet from the base of the sign?
3.
Ken swims diagonally across a swimming pool that is 25 feet wide and 60 feet long. Dirk
swims the length of the pool. Who swims the longer distance and by how much? (a
diagonal cuts a rectangle into two congruent right triangles).
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1.
3
Draw a right triangle and label the sides as indicated in each problem. Use the Pythagorean
property to compute the missing measurement.
Using the Pythagorean property, compute the measurement of each missing leg. Show all
work for this section on another sheet of paper!
Leg
Leg
Hypotenuse
Leg
Leg
1.
18 in.
30 in.
7.
2.
40 mm.
41 mm.
8.
60 in.
100 in.
45 mm.
53 mm.
3.
12 cm.
20 cm.
9.
4.
3 m.
5 m.
10.
5.
12 ft.
15 ft.
11.
6.
15 mm.
17 mm.
12.
54 ft.
Hypotenuse
90 ft.
7.0 ft.
7.4 ft.
4.8 mm.
2.4 m.
7.3 mm.
4 m.
Triangle XYZ is an isosceles triangle (two sides the same length). If we draw the altitude from
point Z to the base and create point T, we form two congruent right triangles.
1. Name the two right triangles formed.
2. What is the measure of the hypotenuse of each triangle?
3. What is the measure of each base of each triangle?
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4
4. Using these dimensions, find the measure of the altitude of the original
triangle to the nearest hundredth.
2. How long in the table?
3. How far is it across the pond?
4. How long is the ramp?
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1. How high will the ladder reach?
5
State an equation that can be used to answer each question. Then solve, round answers to the
nearest tenth.
Draw a picture to go with each word problem. Show all your work and answer each question in
a sentence.
5. A receiver runs down the football field parallel to the sideline for 48 yards. He makes a
sharp turn and runs perpendicular to the sideline for 14 yards. How far is he from the place he
started?
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6
6. The acceleration ramp for the skateboard competition is 20 meters long and extends 15
meters from the base of the starting point. How high is the ramp?
7. Mr. Money is going to wash the windows in his house over the weekend. The bottom of his
windows are 24 feet off the ground. He has a flower garden around his house, so the closest he
can place his ladder is seven feet from the wall. How long should his ladder be if he wants to
place it seven feet from the wall and have it reach 24 feet up the wall?
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8. Mrs. Dunford wants to buy a new 40-inch TV that was advertised to be on sale over the
Memorial Day Weekend. The length along the bottom of the TV is 24 inches. How tall is the TV
that Mrs. Dunford wants to buy?