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9-12 Integrated Math 2 Unit 2 Lesson 11

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Unit 2, Lesson 11

Splitting Triangle Sides with Dilation (Part 2)

$Course Icon$

Integrated Math 2

Practice

Problem 1

Segment \(A’B’\) is parallel to segment \(AB\).

What is the length of segment \(AB\)?
What is the length of segment \(B’B\)?

<p>Triangle A B C.</p> — $\overline{AB} \parallel \overline{A'B'}$

Problem 2

Explain how you know that segment \(DE\) is not parallel to segment \(BC\).

<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>

Problem 3

In right triangle \(ABC\), \(AC=4\) and \(BC=5\). A new triangle \(DEC\) is formed by connecting the midpoints of \(AC\) and \(BC\).

What is the area of triangle \(ABC\)?
What is the area of triangle \(DEC\)?
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>

Problem 4

ForLesson 10: Other Conditions for Triangle Similarity

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.

Problem 5

ForLesson 10: Other Conditions for Triangle Similarity

Are triangles \(ABC\) and \(DEF\) similar? Show or explain your reasoning.
If possible, find the length of \(EF\). If not, explain why the length of \(EF\) 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>

Problem 6

ForLesson 9: Conditions for Triangle Similarity

What is the length of segment \(DF\)?

<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>

Problem 7

ForLesson 3: Measuring Dilations

The triangle \(ABC\) is taken to triangle \(A’B’C’\) 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.

\(\frac12\)
\(\frac89\)
1
\(\frac32\)
2