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9-12 Integrated Math 2 Unit 2 Lesson 18

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 •Lesson 18

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Lesson 18

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Unit 2, Lesson 18

Reflection Similarity

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Integrated Math 2

Practice

Problem 1

Lin is playing handball and wants the ball to bounce off wall and land at . Where on the wall should she aim if she's standing at point ?

<p>Rectangular handball court.</p>

7.8 feet away from point .
13.3 feet away from point .
Anywhere along the wall because all of the triangles will be similar.

Problem 2

You want to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the yellow stripe 9 ball into the top middle pocket.

How can you check to see if your bank shot works?

<p>Drawing of pool table.</p>

Problem 3

Mai is playing a game with a class of second graders. Mai knows that she is exactly 120 inches from the mirror on the floor. She has students stand so that she can just see the top of their heads and then guesses their heights. The students are amazed!

<p>Diagram of 2 stick figures.</p>

How is Mai so accurate? What is the height, , of the student?

Problem 4

ForLesson 17: Finding All the Unknown Values in Triangles

In the right triangles shown, the measure of angle is the same as the measure of angle . What is the length of side ?

<p>Two right triangles, A B C and E B D. Angles C and D are right angles and D is above C on B C. Side A B is 5, A C is 3 and D E is 2. Angle A B C is congruent to angle E B D.</p>

Problem 5

ForLesson 17: Finding All the Unknown Values in Triangles

In right triangle , angle is a right angle, , and . What is the length of ?

Problem 6

ForLesson 16: Proving the Pythagorean Theorem

Fill in the blanks to complete the proof of the Pythagorean Theorem:

<p>Triangle with sides a, b, and c. Right angle between a and b. Segment h drawn from vertex between a and b and meets c at a right angle. H splits c into 2 lengths labeled x and y. X is adjacent to a.</p>

can be rewritten as and can be written as . So, . By factoring, . We know that . So, .

Problem 7

ForLesson 15: Using the Pythagorean Theorem and Similarity

In right triangle , altitude with length is drawn to its hypotenuse. We also know that and . What is the length of ?

<p>Right triangle A B C, an altitude C D with length h is drawn to its hypotenuse. </p>

Problem 8

ForLesson 14: Practice with Proportional Relationships

Match each vocabulary term with its definition.

Scale Drawing
Scale Factor
Dilation
Similar Figures
Angle-Angle Similarity Theorem

There is a sequence of rigid motions and dilations that takes the first figure onto the second.
When 2 angles of one triangle are congruent to 2 angles of a second triangle, the 2 triangles will be similar.
A transformation using a center and scale factor that takes a point to another point along the ray whose distance is times farther from than is.
A drawing in which all lengths in the drawing correspond to lengths in the object by the same scale.
A constant multiple by which all lengths of the original figure are multiplied.

Problem 9

ForLesson 8: Are They All Similar?

Clare and Diego are discussing the quadrilaterals. Clare thinks the quadrilaterals are similar because the side lengths are proportional. Diego thinks they need more information to know for sure if they are similar. Do you agree with either of them? Explain your reasoning.

<p>Quadrilateral W X Y Z. W X, 3. X Y, 9. Y Z, 3. Z W, 9.<br>
</p>

<p>Quadrilateral A B C D. Length of A B is 2, A D is 6, B C is 6, and C D is 2.</p>