Ratios & Proportions of Line Segments

Presentation

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Mathematics

•

10th Grade

•

Medium

•

CCSS

HSG.SRT.A.2, 7.RP.A.2A, HSG.SRT.B.4

Standards-aligned

Tom Giles

Used 4+ times

FREE Resource

11 Slides • 11 Questions

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?

$\frac{24}{12}=\frac{6}{x}$

$\frac{24}{6}=\frac{12}{x}$

$\frac{24}{12}=\frac{x}{6}$

Fill in the Blanks

Example 1, Part 2:

A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad's shadow?

Type answer...

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.

Fill in the Blanks

Example 2:

Triangles EFG and QRS are similar. The length of the sides of EFG are 144, 128, and 112. The length of the smallest side of QRS is 280, what is the length of the longest side of QRS?

Type answer...

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

Type response here

Fill in the Blanks

Example 3, Part 2:

A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How tall is the lamp post?

Type answer...

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.

Fill in the Blanks

Example 4, Part 2:

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. What is the perimeter of TUV?

Type answer...

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)

Fill in the Blanks

Using the diagram in the previous slide, solve for x and y respectively. Seperate your answers with a comma.

Type answer...

Fill in the Blanks

Solve the proportion.

$\frac{m}{m+2}=\frac{m-2}{m-4}$

Type answer...

Proportion and Similarity Practice

With Line Segments

February 15, 2023

Dr. Tom Giles

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