Lesson 10: Practice Problems

Problem 1

Triangle $A B C$ is dilated using $D$ as the center of dilation with scale factor 2.

The image is triangle $A^{'} B^{'} C^{'}$ . Clare says the two triangles are congruent, because their angle measures are the same. Do you agree? Explain how you know.

Dilation point D and triangles ABC and larger triangle A'B'C'.

Problem 2

On graph paper, sketch the image of quadrilateral $P Q R S$ under the following dilations:

The dilation centered at $R$ with scale factor 2.
The dilation centered at $O$ with scale factor $\frac{1}{2}$ .
The dilation centered at $S$ with scale factor $\frac{1}{2}$ .

A grid with quadrilateral PQRS and point O 3 units below point Q.

Problem 3

Quadrilateral $A B C D$ is dilated with center $(0, 0)$ , taking $B$ to $B^{'}$ . Draw $A^{'} B^{'} C^{'} D^{'}$ .

A quadrilateral with points A (-2, 3), B (3, 1), C (1, -1), D (-3, -2). Point B' is at (6, 2 )

Problem 4

Triangles $B$ and $C$ have been built by dilating Triangle $A$ .

Find the center of dilation.
Triangle $B$ is a dilation of $A$ with approximately what scale factor?
Triangle $A$ is a dilation of $B$ with approximately what scale factor?
Triangle $B$ is a dilation of $C$ with approximately what scale factor?

Problem 5

Here is a triangle.
- Draw the dilation of triangle $A B C$ , with center $(0, 0)$ , and scale factor 2. Label this triangle $A^{'} B^{'} C^{'}$ .
- Draw the dilation of triangle $A B C$ , with center $(0, 0)$ , and scale factor $\frac{1}{2}$ . Label this triangle $A^{″} B^{″} C^{″}$ .
Is $A^{″} B^{″} C^{″}$ a dilation of triangle $A^{'} B^{'} C^{'}$ ? If yes, what are the center of dilation and the scale factor?

Problem 6 From Unit 1 Lesson 12

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

Two lines cut by a third line. An intersecting angle 35 deg on one line and 27 deg on the other line in the same position