Unit 2, Lesson 5

Splitting Triangle Sides with Dilation (Part 1)

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Integrated Math 2

Practice

Problem 1

Student Task Statement

What is the measure of angle ?

<p>Triangle A B C with segment A’ B’ drawn. A A’ is 2 and A’ C is 4. B B’ is 3 and B’ C is 6. Angle B is 40 degrees.</p>

Practice

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Problem 2

Student Task Statement

Triangle is formed by connecting the midpoints of the sides of triangle . The lengths of the sides of are shown. What is the length of ?

<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>

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Problem 3

ForLesson 4: Dilating Lines and Angles

Student Task Statement

Angle is taken by a dilation with center and a scale factor of to angle . The measure of angle is . What is the measure of angle ?

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Problem 4

ForLesson 4: Dilating Lines and Angles

Student Task Statement

Draw 2 lines that could be the image of line by a dilation. Label the lines and .

<p>2 intersecting lines labeled o and m.</p>

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Problem 5

ForLesson 3: Measuring Dilations

Student Task Statement

Is it possible for polygon to be dilated to figure ? Explain your reasoning.

<p>Polygon V W X Y Z. Side V W labeld 8. Side W X labeled 10. Side X Y labeled 6. Side Y Z labeled 8. Side Z V labeled 12.<br>
</p>

<p>Polygon A B C D E. Side A B labeled 4. Side B C labeled 5. Side C D labeled 3. Side D E labeled 4. Side E A labeled 10.<br>
</p>

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Problem 6

ForLesson 2: Scale of the Solar System

Student Task Statement

Triangle is scaled, and the image is . Write 2 equations that could be used to solve for .

<p>Triangles X Y Z and X prime Y prime Z prime. Side X Y is 8 and side X Z is 5. Side X prime Y prime is 3 and side X prime Z prime is a.</p>

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Problem 7

ForLesson 12: Proofs about Quadrilaterals

Student Task Statement

Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that is a parallelogram and angle is a right angle, write a statement that will help prove that angle is also a right angle.
Han then states that the 2 triangles created by diagonal must be congruent. Help Han write a proof that triangle is congruent to triangle .

<p>Quadrilateral EFGH with angle HEF as a right angle. Line segments EG and HF intersect at point D.</p>

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Splitting Triangle Sides with Dilation (Part 1)

Practice

Problem 1

Student Task Statement

Problem 2

Student Task Statement

Problem 3

Student Task Statement

Problem 4

Student Task Statement

Problem 5

Student Task Statement

Problem 6

Student Task Statement

Problem 7

Student Task Statement

Lesson 5 Resources