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9-12 Integrated Math 2 Unit 2 Lesson 15

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Unit 2, Lesson 15

Using the Pythagorean Theorem and Similarity

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Integrated Math 2

Practice

Problem 1

In right triangle , altitude is drawn to its hypotenuse. Select all triangles that must be similar to triangle .

<p>Right triangle A B C has right angle C and altitude C D drawn to the hypotenuse. Ange B D C is a right angle.</p>

Problem 2

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

<p><strong>Right triangle A B C, angle C marked as right. Altitude C D drawn to hypotenuse A B. Segment C D labeled h. Segment B D labeled 3. Segment D A labeled 12.</strong></p>

Problem 3

In triangle (not a right triangle), altitude is drawn to side . The length of is . Which of the following statements must be true?

<p>Triangle A B C is not a right triangle. Altitude C D is drawn to side A B and is length h. Side A C is b, side B C is a and A D is e. Angle A C B is 75 degrees. Side A B is length c.</p>

The measure of angle is the same measure as angle .

Problem 4

ForLesson 14: Practice with Proportional Relationships

Quadrilateral is similar to quadrilateral . Write 2 equations that could be used to solve for missing lengths.

Problem 5

ForLesson 11: Splitting Triangle Sides with Dilation (Part 2)

Segment is parallel to segment .

What is the length of segment ?
What is the length of segment ?

<p><strong>Triangles A B C and A prime B prime C. Lengths as follows: Directed segment A B, 20. Directed segment A prime B prime, 8. Segment B prime C, 6. Segment A prime C, 12.</strong></p>

Problem 6

ForLesson 14: Practice with Proportional Relationships

Lines and are both vertical. What is the length of ?

<p>Line A B is horizontal and has 3 points, A, B and D. Lines B C and D E are vertical. Line A C goes through C on B C and E on D E. A B is 3, B C is 2 and D E is 5.<br>
</p>

4.5
5
7.5
10

Problem 7

ForLesson 5: Splitting Triangle Sides with Dilation (Part 1)

Triangle is formed by connecting the midpoints of the sides of triangle . Select all true statements.

<p>Triangles A B C and D E F. D is the midpoint of segment A B. E is the midpoint of segment B C. F is the midpoint of segment A C. Line D E has length 2, Line E F has length 3, Line D F has line 4.<br>
</p>

Triangle is congruent to triangle .

.

Triangle is similar to triangle .

The area of triangle equals .

Triangle is congruent to triangle .

is congruent to .

The length of is 8.

The length of is 6.