Unit 4, Lesson 2

Half a Square (Optional)

Geometry

Practice

Problem 1

Find the length of the legs.

<p>Triangle. An angle is marked as a right angle. Another angle is labeled 45 degrees. The side opposite the right angle is labeled 4.</p>

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

Not enough information

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Problem 2

What is the length of the diagonal of this square?

<p>A four sided figure. Each side has a single tick mark. Each angle is marked as a right angle. The top of the figure is labeled 1.</p>

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Problem 3

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

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Problem 4

ForLesson 1: Angles and Steepness

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.

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Problem 5

ForLesson 1: Angles and Steepness

Clare and Han are discussing how to find the unknown 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 unknown sides.

<p>Two right triangles. Triangle A B C has right angle B, side A B is 2 point 5 and B C is 6. Triangle D E F has right angle E, side E F is 5 and D F is 13.</p> — \(\angle {BAC} \cong \angle {EFD}\)

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Problem 6

ForLesson 16: Finding All the Unknown Values in Triangles

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

1 cm
2 cm
7 cm
49 cm

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Problem 7

ForLesson 10: Other Conditions for Triangle Similarity

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

<p><strong>Two triangles, A B C and D E F. Angle and side labels as follows: Angle A B C, 82. Angle B A C, 55. Side B C, 12. Side A C, 14. Angle D F E, 43. Angle E D F, 55. Side D F, 21.</strong></p>

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Problem 8

ForLesson 7: Reasoning about Similarity with Transformations

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.

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Half a Square (Optional)

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Lesson 2 Resources