Lesson 14

Side Length Quotients in Similar Triangles

Let’s find missing side lengths in triangles.

Problem 1

These two triangles are similar. What are \(a\) and \(b\)? Note: the two figures are not drawn to scale.

Two triangles. First with sides 10, 15, b. Sides with length 10 and 15 form an obtuse angle. Second with sides 4, a, 9. Sides with length 4 and a, form an obtuse angle.

Problem 2

Here is triangle \(ABC\). Triangle \(XYZ\) is similar to \(ABC\) with scale factor \(\frac 1 4\).

Triangle A, B C. Side A, B length 4, side B C length 7, side C A, length 5.
  1. Draw what triangle \(XYZ\) might look like.
  2. How do the angle measures of triangle \(XYZ\) compare to triangle \(ABC\)? Explain how you know.

  3. What are the side lengths of triangle \(XYZ\)?

  4. For triangle \(XYZ\), calculate (long side) \(\div\) (medium side), and compare to triangle \(ABC\).

Problem 3

The two triangles shown are similar. Find the value of \(\frac d c\).

Two right triangles with each hypotenuse on the same line. First has horizontal side length 7 point 5, vertical side length 9. Second has horizontal side length d and vertical side length c.

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.

Coordinate plane, x, negative 9 to 3, y, negative 2 to 7.
(From Unit 2, Lesson 10.)

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.

Six L-shaped figures on a grid, labeled A, B, C, D, E, and F. 
(From Unit 2, Lesson 2.)

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.

(From Unit 2, Lesson 7.)