Lesson 13: Practice Problems

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 $B C$ is parallel to line $D E$ .

Triangle ABC with smaller triangle inside labeled ADE.

Explain why $△ A B C$ is similar to $△ A D E$ .

Problem 4

The quadrilateral $P Q R S$ in the diagram is a parallelogram. Let $P^{'} Q^{'} R^{'} S^{'}$ be the image of $P Q R S$ after applying a dilation centered at a point $O$ (not shown) with scale factor 3.

Which of the following is true?

$P^{'} Q^{'} = P Q$
$P^{'} Q^{'} = 3 P Q$
$P Q = 3 P^{'} Q^{'}$
Cannot be determined from the information given

Problem 5 From Unit 1 Lesson 5

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

Quadrilateral P and Q. Coordinate of P: (4,1), (6,6), (3,4),(4,4). Coordinate of Q: (7,-4), (12,-5), (10,-3) (10,-4).

Problem 6

Polygon $B$ is a scaled copy of Polygon $A$ .

Pentagon A clockwise from the top has length 2.5, angle unknown, length 2.5, angle unknown, 2 unknown lengths, length 1.5. Pentagon B has top length 5, angle of 53 degrees, unknown length, angle of 82 degrees, and all the rest unknown.

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 $A$ .