Lesson 14: Practice Problems

Problem 1

These two triangles are similar.

A triangle with side length 10, 15, and b. A second triangle with side length a, 4, and 9.

What are $a$ and $b$ ? Note: the two figures are not drawn to scale.

Problem 2

Here is triangle $A B C$ . Triangle $X Y Z$ is similar to $A B C$ with scale factor $\frac{1}{4}$ .

A triangle ABC with side length 4, 5, 7.

Draw what triangle $X Y Z$ might look like.
How do the angle measures of triangle $X Y Z$ compare to triangle $A B C$ ? Explain how you know.
What are the side lengths of triangle $X Y Z$ ?
For triangle $X Y Z$ , calculate (long side) $\div$ (medium side), and compare to triangle $A B C$ .

Problem 3

The two triangles shown are similar. Find the value of $\frac{d}{c}$ .

A triangle with legs 7.5 and 9 and a similar triangle with legs d (corresponding to 7.5) and c (corresponding to 9)

Problem 4

The diagram shows two nested triangles that share a vertex. Find a center and a scale factor for a dilation that would move the larger triangle to the smaller triangle.

Two nested triangles with a vertex at (-1,1). Small triangle coordinates: (-2,1), (-2,2). Larger triangle: (-6,1), (-6, 6)

Problem 5

Which is a scaled copy of Polygon A? Identify a pair of corresponding sides and a pair of corresponding angles. Compare the areas of the scaled copies.

A grid with six L shaped polygons labeled A-F in differing sizes.

Problem 6

A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same? Explain your reasoning.