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9-12 Geometry Unit 3 Lesson 11

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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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

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Unit 3, Lesson 11

Splitting Triangle Sides with Dilation (Part 2)

Geometry

Practice

Problem 1

Student Task Statement

Segment is parallel to segment .

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

<p>Triangle A B C.</p>

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Problem 2

Student Task Statement

Explain how you know that segment is not parallel to segment .

<p>Triangle A B C has segment D E, with D on A B and E on A C. A D is 4, D B is 2, A E is 9 and E C is 5 and D E is 11.</p>

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Problem 3

Student Task Statement

In right triangle , and . A new triangle is formed by connecting the midpoints of and .

What is the area of triangle ?
What is the area of triangle ?
Does the scale factor for the side lengths apply to the area as well?

<p>Right triangle A B C has right angle C. A C is 4 and B C is 5. Point D is at the midpoint of A C and point E is at the midpoint of B C.</p>

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Problem 4

ForLesson 10: Other Conditions for Triangle Similarity

Student Task Statement

Which of these statements is true?

To know whether 2 triangles are similar, it is enough to know the measure of 1 angle.
To know whether 2 triangles are similar, it is enough to know the length of 1 side.
To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.
To know whether 2 triangles are similar, it is enough to know the measure of 2 sides in each triangle.

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Problem 5

ForLesson 10: Other Conditions for Triangle Similarity

Student Task Statement

Are triangles and similar? Show or explain your reasoning.
If possible, find the length of . If not, explain why the length of cannot be determined.

<p>Triangle A B C and D E F. Length of A B is 9, B C is 6, and D E is 12. Angle A is 60 degrees, angle C is 20 degrees, angle D is 60 degrees, and angle E is 100 degrees.</p>

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Problem 6

ForLesson 9: Conditions for Triangle Similarity

Student Task Statement

What is the length of segment ?

<p>2 triangles, A B C and D E F. Angles A and D are 68 degrees. Angles B and F are 28 degrees. Side A C is 2. Side A B is 4. Side D E is 8.</p>

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Problem 7

ForLesson 3: Measuring Dilations

Student Task Statement

The triangle is taken to triangle by a dilation. Select all of the scale factors for the dilation that would result in an image that was smaller than the original figure.

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Lesson 11 Resources

Student Materials

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