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7.7 Similarity in Right Triangles (Due 5/6/22)

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Last updated 8 days ago
49 questions
Note from the author:
Essential Question: How can you prove triangles are similar? Learning Target: Students will be able to determine if triangles are similar by creating a proportion comparing the corresponding sides. Complete the entire document and show all work for full credit
Essential Question: How can you prove triangles are similar? Learning Target: Students will be able to determine if triangles are similar by creating a proportion comparing the corresponding sides. Complete the entire document and show all work for full credit
Essential Question: How can we use the properties of similar right triangles to solve real-world problems and make predictions?

Learning Target: By the end of this lesson, students will be able to: Identify and apply the properties of similar right triangles to solve problems involving proportions and side lengths.

Complete the entire document and use full sentences when prompted for full credit.

Responses without work will receive no points.

Remember to upload work from paper when prompted to receive credit.

Day 1 (4/23/26)

List of the first 25 perfect squares.


Required
10
Required
10
Required
5
Required
5
Required
5
Required
5
Required
5
Required
5

Concept Review

Simplifying Radicals
Required
20
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
4
Required
4
Required
10
Required
5
Required
5
Required
5
Required
5
Required
5
Required
10

Day 2 (4/24/26)

Similarity in Right Triangles

Required
5
Question 29
29.
Use the diagram to complete each equation.
Complete the proportion.
_______ =_______

Cross multiply and complete this equation.

e²=_______

Solve for the altitude e
e=_______

Right Triangle Similarity

(When you have all 3 Sides of a Right Triangle)

Required
10
Question 30
30.
Solve for x and y. (Round your answer to the nearest tenth.)

x=_______

y=_______
Required
10
Question 31
31.

Solve for x. (Round your answer to the nearest tenth.)

Right Triangle Similarity:

Altitude and Hypotenuse Theorem


Required
10
Question 32
32.

Solve for x. (Round your answer to the nearest tenth.)

Required
10
Required
10
Required
10
Required
5
Required
10
Required
10
Required
10
Required
10
Required
10

More Right Triangles

Required
30
Question 42
42.
Required
30
Required
30
Required
30
Required
30

Learning Log

Required
5
Question 47
47.

Required
5
Question 48
48.

Required
10
Question 49
49.

Simplifying Radicals




Question 1
1.

Describe in your own words; What is a perfect square number?

Question 2
2.

When you simplify a square root and it is not a "perfect square," what do you do?

Question 3
3.

What is the largest perfect square factor of 48?

Question 4
4.

What is the square root of 48?

Question 5
5.

What is the largest perfect square factor of 63?

Question 6
6.

What is the square root of 63?

Question 7
7.

What is the largest perfect square factor of 72?

Question 8
8.

What is the square root of 72?

Pythagorean Theorem

Question 9
9.

Fill in the missing steps.

Question 10
10.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.

_______
Question 11
11.

Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.

Question 12
12.

Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.

Question 13
13.

Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.

Question 14
14.

Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.

Question 15
15.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.
_______
Question 16
16.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.
_______
Question 17
17.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.
_______
Question 18
18.

Scott is using a 12-foot ramp to help load furniture into the back of a moving truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck?

Question 19
19.

A 35-foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 14 feet from the base of the flagpole, how tall is the flagpole?

Geometric Mean

Question 20
20.
Find the pattern and fill in missing numbers.

5,_______,15, 20, _______
Question 21
21.
Find the pattern and fill in missing numbers.

5,_______,125, 625, _______
Question 22
22.

What was the difference between the pattern from question 20 and question 21?

Question 23
23.
Find the number the middle between these two numbers using multiplication:

2 _______ 200

This is called the geometric mean between 2 and 200.
Question 24
24.

Find the geometric mean between 7 and 15. (Remember to simplify your radical. Do not use decimals)

Question 25
25.

Find the geometric mean between 5 and 20. (Remember to simplify your radical. Do not use decimals)

Question 26
26.

Find the geometric mean between 3 and 12. (Remember to simplify your radical. Do not use decimals)

Question 27
27.

Find the geometric mean between 8 and 13. (Remember to simplify your radical. Do not use decimals)

Question 28
28.

What does the geometric mean find?

Answer using your own words.

Question 33
33.

Solve for x. (Round your answer to the nearest tenth.)

Question 34
34.

Solve for x. (Round your answer to the nearest tenth.)

Question 35
35.

Solve for x. (Round your answer to the nearest tenth.)

Right Triangle Similarity:

Hypotenuse and Leg Theorem

Question 36
36.

Use the diagram to complete each equation.

Question 37
37.

Solve for x. (Round your answer to the nearest tenth.)

Question 38
38.

Solve for x. (Round your answer to the nearest tenth.)

Question 39
39.

Solve for x. (Round your answer to the nearest tenth.)

Question 40
40.

Solve for x. (Round your answer to the nearest tenth.)

Question 41
41.

Solve for x. (Round your answer to the nearest tenth.)

Find the values of x, y, and z

(Round your answer to the nearest tenth.)

x=_______
y=_______
z= _______
Question 43
43.
Find the values of x, y, and z


(Round your answer to the nearest tenth.)

x=_______
y=_______
z= _______
Question 44
44.
Find the values of x, y, and z

(Round your answer to the nearest tenth.)

x=_______
y=_______
z= _______
Question 45
45.
Find the values of x, y, and z

(Round your answer to the nearest tenth.)

x=_______
y=_______
z= _______
Question 46
46.
Find the values of x, y, and z

(Round your answer to the nearest tenth.)

x=_______
y=_______
z= _______