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

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49 questions
Note from the author:
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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

Day 1 3/13/25

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.

Concept Review

Simplifying Radicals

List of the first 25 perfect squares.


Simplifying Radicals




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Question 1
1.

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

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10
Question 2
2.

When you simplifying 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?

Question 9
9.

What is the largest perfect square factor of 147?

Question 10
10.

What is the square root of 147?

Question 11
11.

Simplify this radical. (To simplify this radical, find the square number(s) that are factors).

Question 12
12.

Simplify this radical. (To simplify this radical, find the square number(s) that are factors).

Question 13
13.

Simplify this radical. (To simplify this radical, find the square number(s) that are factors).

Pythagorean Theorem

Question 14
14.

Fill in the missing steps.

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.

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

Question 19
19.

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

Question 20
20.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.
_______
Question 21
21.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.
_______
Question 22
22.
Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.
_______
Question 23
23.

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 24
24.

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?

Day 2 (3/17/25)

Pythagorean Theorem


Similarity in Right Triangles

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 7 and 15. (Remember to simplify your radical. Do not use decimals)

Question 27
27.

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

Question 28
28.

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

Question 29
29.

Use the diagram to complete each equation.

Question 30
30.

Use the diagram to complete each equation.

Right Triangle Similarity

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

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Question 31
31.

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

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Question 32
32.
Solve for x and y. (Round your answer to the nearest tenth.)

x=_______

y=_______

Right Triangle Similarity:

Altitude and Hypotenuse Theorem


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Question 33
33.

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

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Right Triangle Similarity:

Hypotenuse and Leg Theorem

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More Right Triangles

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Question 42
42.
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Concept Review

Question 47
47.

Find the measure of ∠B? For help click here.

Question 48
48.
Which two angles are the remote interior angles to ∠W? For help click here.


∠_______
∠_______
Question 49
49.
Find the measure of all three angles. For help click here.

_______
_______
_______
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.)

Question 36
36.

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

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= _______