Lesson 11

Splitting Triangle Sides with Dilation, Part 2

  • Let’s investigate parallel segments in triangles.

Problem 1

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

  1. What is the length of segment \(AB\)?
  2. What is the length of segment \(B’B\)?
Triangle A B C.

Problem 2

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

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.

Problem 3

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

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.
  1. What is the area of triangle \(ABC\)?
  2. What is the area of triangle \(DEC\)?
  3. Does the scale factor for the side lengths apply to the area as well?

Problem 4

Which of these statements is true?

A:

To know whether 2 triangles are similar, it is enough to know the measure of 1 angle.

B:

To know whether 2 triangles are similar, it is enough to know the length of 1 side.

C:

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

D:

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

(From Unit 3, Lesson 10.)

Problem 5

  1. Are triangles \(ABC\) and \(DEF\) similar? Show or explain your reasoning. 
  2. If possible, find the length of \(EF\). If not, explain why the length of \(EF\) cannot be determined. 
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.
(From Unit 3, Lesson 10.)

Problem 6

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

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.
(From Unit 3, Lesson 9.)

Problem 7

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.

A:

\(\frac12\)

B:

\(\frac89\)

C:

1

D:

\(\frac32\)

E:

2

(From Unit 3, Lesson 3.)