# Lesson 2

Half a Square

### Problem 1

Find the lengths of the legs.

\(4\sqrt{2}\) units

\(\frac{4}{\sqrt{2}}\) units

4 units

Not enough information

### Solution

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### Problem 2

What is the length of the diagonal?

### Solution

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### Problem 3

A square has a diagonal of length 5 cm. What is the area of the square?

### Solution

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### Problem 4

Priya is teaching her younger cousin to ride a bike. She wants to stay on roads that are not too steep and easy enough for a new bike rider. She has decided the roads must have an angle less than or equal to 7 degrees. A 7 degree angle in a right triangle has a \(3:25\) ratio for the legs. List the legs of 2 right triangles that would be safe for a new bike rider.

### Solution

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(From Unit 4, Lesson 1.)### Problem 5

Clare and Han are discussing how to find the missing lengths. Clare says she is using similarity. Han says he is using the Pythagorean Theorem.

- Do you agree with either of them? Show or explain your reasoning.
- Find the missing sides.

### Solution

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(From Unit 4, Lesson 1.)### Problem 6

In right triangle \(ABC\), angle \(C\) is a right angle, \(AB\) is 25 units long, and \(BC\) is 24 units long. What is the length of \(AC\)?

1

2

7

49

### Solution

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(From Unit 3, Lesson 15.)### Problem 7

- Find the length of \(EF\).
- Find the measure of angle \(E\).

### Solution

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(From Unit 3, Lesson 10.)### Problem 8

Determine if each statement must be true, could possibly be true, or definitely can't be true. Explain or show your reasoning.

- Isosceles triangles are similar.
- Equilateral triangles are similar.

### Solution

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(From Unit 3, Lesson 7.)