Illustrative Mathematics | v.360 Curriculum

Problem 1

For each pair of triangles, some of the angle measures are given in degrees. Use the information to decide if the triangles are similar or not. Explain how you know.

Triangle A: 53, 71, \(\underline{\hspace{.5in}}\); Triangle B: 53, 71, \(\underline{\hspace{.5in}}\)
Triangle C: 90, 37, \(\underline{\hspace{.5in}}\); Triangle D: 90, 53, \(\underline{\hspace{.5in}}\)
Triangle E: 63, 45, \(\underline{\hspace{.5in}}\); Triangle F: 14, 71, \(\underline{\hspace{.5in}}\)
Triangle G: 121, \(\underline{\hspace{.5in}}\), \(\underline{\hspace{.5in}}\); Triangle H: 70, \(\underline{\hspace{.5in}}\), \(\underline{\hspace{.5in}}\)

Problem 2

Draw 2 equilateral triangles that are not congruent.
Measure the side lengths and angles of your triangles. Are the 2 triangles similar?
Do you think 2 equilateral triangles will be similar always, sometimes, or never? Explain your reasoning.

Problem 3

In the figure, line segment \(BC\) is parallel to line segment \(DE\).

Explain why triangle \(ABC\) is similar to triangle \(ADE\).

Two triangles. First, A, B C. Then triangle A, D E where D lies on side A, B and E lies on side A, E.<br>

Problem 4

ForLesson 10: Dilations on a Square Grid

The quadrilateral \(PQRS\) in the diagram is a parallelogram.

Let \(P’Q’R’S’\) be the image of \(PQRS\) after applying a dilation centered at a point \(O\) (not shown) with scale factor 3.

Which of the following is true?

\(P’Q’= PQ\)
\(P’Q’=3PQ\)
\(PQ=3P’Q’\)
\(P’Q’=\frac13PQ\)

Problem 5

ForLesson 5: Describing Transformations

Describe a sequence of transformations for which Quadrilateral P is the image of Quadrilateral Q.

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