Side Length Quotients in Similar Triangles

Multiple Choice

These 2 triangles are similar. What are $$a$$ and $$b$$ ? Note: the 2 figures are not drawn to scale.

• a = 30, b = 10
• a = 22.5, b = 6.67
• a = 15, b = 5
• a = 10, b = 20

Draw

Draw what triangle $$XYZ$$ might look like. Triangle $$XYZ$$ is similar to $$ABC$$ with scale factor $$\frac 1 4$$ .

Open Ended

How do the angle measures of triangle $$XYZ$$ compare to triangle $$ABC$$ ? Explain how you know. Triangle $$XYZ$$ is similar to $$ABC$$ with scale factor $$\frac 1 4$$ .

Multiple Choice

What are the side lengths of triangle XYZ if it is similar to triangle ABC with side lengths 4, 5, and 7, and a scale factor of 1/4?

• 0.5, 1, 1.75
• 1, 1.25, 1.75
• 1, 1.5, 2
• 2, 2.5, 3

Multiple Choice

For triangle $$XYZ$$ , calculate (long side) $$\div$$ (medium side), and compare to triangle $$ABC$$ . Triangle $$XYZ$$ is similar to $$ABC$$ with scale factor $$\frac 1 4$$ . What is the ratio for triangle $$XYZ$$ ?

• 1.6
• 1.4
• 1.2
• 2.0

Multiple Choice

The 2 triangles shown are similar. Find the value of $$\frac d c$$ .

• rac{2}{3}
• \frac{5}{6}
• rac{4}{5}
• rac{3}{4}

Open Ended

Explain how you know that Triangle B is not similar to Triangle A. Triangle A has side lengths 3 units, 4 units, and 5 units. Triangle B has side lengths 6 units, 7 units, and 8 units.

Multiple Choice

Which of the following sets of side lengths could be for Triangle B so that it is similar to Triangle A, which has side lengths 3 units, 4 units, and 5 units?

• 5, 5, 5
• 2, 3, 4
• 1, 1, 1
• Any set of side lengths that are multiples of 3, 4, and 5, such as 6, 8, and 10.