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.