Lesson 13
Similar Triangles
Let’s look at similar triangles.
Problem 1
In each pair, some of the angles of two triangles in degrees are given. Use the information to decide if the triangles are similar or not. Explain how you know.

Triangle A: 53, 71, ___; Triangle B: 53, 71, ___

Triangle C: 90, 37, ___; Triangle D: 90, 53, ___

Triangle E: 63, 45, ____; Triangle F: 14, 71, ____

Triangle G: 121, ___, ___; Triangle H: 70, ___, ___
Problem 2

Draw two equilateral triangles that are not congruent.
 Measure the side lengths and angles of your triangles. Are the two triangles similar?

Do you think two equilateral triangles will be similar always, sometimes, or never? Explain your reasoning.
Problem 3
In the figure, line \(BC\) is parallel to line \(DE\).
Explain why \(\triangle ABC\) is similar to \(\triangle ADE\).
Problem 4
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?
\(P’Q’= PQ\)
\(P’Q’=3PQ\)
\(PQ=3P’Q’\)
Cannot be determined from the information given
Problem 5
Describe a sequence of transformations for which Quadrilateral P is the image of Quadrilateral Q.
Problem 6
Polygon B is a scaled copy of Polygon A.

What is the scale factor from Polygon A to Polygon B? Explain your reasoning.

Find the missing length of each side marked with ? in Polygon B.

Determine the measure of each angle marked with ? in Polygon A.