Ratios & Proportions of Line Segments

Proportion and Similarity Practice

With Line Segments

February 15, 2023

​ Dr. Tom Giles

Line Segments and Distance

Multiple Choice

Example 1, Part 1: 

A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. Which of the following is NOT a proportion that accurately represents the given example?

• $$\frac{24}{12}=\frac{6}{x}$$

• $$\frac{24}{6}=\frac{12}{x}$$

• $$\frac{24}{12}=\frac{x}{6}$$

Line Segments and Distance

On line PQ, to say that point M is between points P and Q means P, Q, and M are collinear and PM + MQ = PQ. 

On , AB = BC = 3 cm. We can say that the segments are congruent segments, or  . Slashes on the figure indicate which segments are congruent.

Example 3

Copy down the diagram. You will be using it for the next two questions

Find Distance Using Segment Addition and Algebra

Multiple Choice

Example 3, Part 1:

A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. Which of the following is a proportion that accurately represents the given situation?

• $$\frac{x}{160}=\frac{360}{90}$$

• $$\frac{x}{160}=\frac{450}{90}$$

• $$\frac{x}{450}=\frac{90}{160}$$

Open Ended

ALGEBRA Find the value of x and RS if S is between R and T.

RS = 5x, ST = 3x, and RT = 48

Fill in the Blanks

Multiple Choice

ALGEBRA Find the value of x and RS if S is between R and T.

RS = 6x, ST = 12, and RT = 72

• RS = 12, x = 8

• RS = 10, x= 10

Distance Between Two Points

The distance between two points on a number line is the absolute value of the difference between their coordinates. If P and Q are on the same line, their distance is the absolute value of their difference. 

Find the distance between each point:

1. Find BD.                   2. Find DG. 

3. Find AF.                    4. Find EF. 

5. Find BG.                   6. Find AG.           

Multiple Choice

Example 4, Part 1:
Triangles IJK and TUV are similar. The length of the sides of IJK are 40, 50, and 24. The length of the longest side of TUV is 275. Which of the following proportions can be used to solve for the perimeter of TUV?

• $$\frac{114}{x}=\frac{50}{275}$$  

• $$\frac{24}{x}=\frac{50}{275}$$  

Distance  Formula

To find the distance between two points in a coordinate plane, you can form a right triangle, and then use the Pythagorean Theorem to find the distance between the two points. The formula on the right shows the distance between two point on the coordinate plane. 

Example 5

Copy down the diagram. You will be using it for the next question

Find the distance between each pair of points.

7. A(–1, 2) and B(–4, 6)       



8. C(5, –3) and D(4, –2)