Proportions and Similarity

Proportions and Similarity

By Heather Eve

​Add to your notes as you go!

This lesson is designed to review ideas that you have seen before, allow you to practice skills that have been difficult so far, and also introduce some new ideas and skills. It is very immportant that you take notes while you work through this lesson.

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

$$\frac{x}{5}=\frac{20}{25}$$  

• 5

• 4

• 3

• 2

Multiple Choice

Determine whether the pair of ratios forms a proportion

• Proportion

• Not a Proportion

Multiple Choice

Determine whether the pair of ratios forms a proportion

• Proportion

• Not a Proportion

Multiple Choice

Determine whether the pair of ratios forms a proportion

• Proportion

• Not a Proportion

​Review and Practice 1: Determining if Two Objects are In Proportion

Strategy:

• Choose two sides from the first object to compare. For example, a big side and a small side, and create a fraction. BIG/small

• ​Choose two MATCHING sides from the second object to compare. Create a fraction. BIG/small

• ​Compare the two fractions you made. If they are the same, hooray! PROPORTIONAL!

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Are the following in proportion?

• Yes
• No

Multiple Choice

Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)

• Yes, similar because they are the same shape and side lengths are proportional.
• No, not similar because they are the same shape, but all side lengths are not proportional.

• Yes, same shape
• Yes, same side length

Multiple Choice

State if the polygons are in proportion (similar).

• Similar

• Not Similar

​Review and Practice 2: Finding the Scale Factor

Strategy:

• AFTER you know two objects are similar/in proportion you can look for scale factor

• ​Choose a side from the first object (circle it if you can). Then choose the matching side from the second object.

• ​Create a fraction with the one you are starting FROM on the bottom. Like this: TO/FROM

• Simplify!​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

If the scale factor is less than one, the new figure will be

• an enlargement
• a reduction (smaller)

• a scale factor
• bigger

Multiple Choice

If the scale factor is greater than one, the new figure will be

• a reduction (smaller)

• an enlargement (bigger)

• a scale
• not proportional

Multiple Choice

What is the scale factor from the large rectangle to the small rectangle?

• $$\frac{3}{2}$$

• $$\frac{2}{3}$$

• $$\frac{24}{15}$$

• $$\frac{8}{5}$$

Multiple Choice

What is the scale factor from ΔDEF to ΔABC?

• 1/2
• 7/3
• 2
• 10/3

Multiple Choice

What is the scale factor from ABCD to MNOP?

• 2/3
• 3/2
• 2
• 3

Multiple Choice

What is the scale factor from small to big of these 2 figures?

• $$\frac{3}{2}$$

• $$-\frac{3}{2}$$

• $$\frac{2}{3}$$

• $$-\frac{2}{3}$$

​Review and Practice 3: Finding a Missing Piece

Strategy:

• AFTER you know two objects are similar/in proportion you can look for missing parts using one of two options

• Option 1: ​Compare parts of the big object to parts of the small object. Set up two fractions. (BIG OBJECT SIDE A) = (BIG OBJECT SIDE B)

  (small object side a) (small object side b)

• ​Option 2: ​Compare parts of an object to parts of the same object. Set up two fractions.

  (BIG OBJECT SIDE A) = (small object side a)

  (BIG OBJECT SIDE B) (small object side b)

• Lastly, cross-multiply and use algebra to find the missing part!​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Solve for x.

• 2

• -14

• -2

• 14

Multiple Choice

The triangles are in proportion (similar). Solve for x.

• 7

• 2

• 4

• 8

Multiple Choice

The triangles are in proportion (similar). Solve for x.

• 34

• 26
  

• 30

• 16
  

Multiple Choice

Solve for x. The polygons are in proportion (similar).

• 9

• 12

• 6

• 10

Multiple Choice

A large Ghirardelli’s bar is 30 cm long and 12 cm wide. A smaller Ghirardelli’s bar is 10 cm long. If the bars are similar, what is the perimeter of the smaller Ghirardelli’s bar?

• 28 cm

• 4 cm

• 30 cm

• 8 cm

Multiple Choice

Find the missing length. The triangles are in proportion (similar).

• 11

• 4

• 7

• 10

​NEW TOPICS

These tips and facts will help you with practice problems you have seen before or are about to try.

​

• A triangle that is part of another triangle with one side parallel will ALWAYS be in proportion!

​

• A triangle that is divided using a bisected angle (for example, two 90 degree angles as shown) will have both PARTS in proportion.

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Which statement must be true?

• $$\frac{PQ}{ST}=\frac{QR}{TR}$$

• PS = TS

• $$\frac{PQ}{ST}=\frac{PS}{SR}$$

• PS = PR

Multiple Choice

Solve for x.

• 6.67

• 15

• 9.60

• 10

Multiple Choice

If a tree casts a 24-foot shadow at the same time that a yardstick casts a 2-foot shadow. Find the height of the tree.

• 36 ft

• 33 ft

• 30 ft

• 28 ft

Multiple Choice

Find the length of NR.

• 72

• 112

• 112.5

• 152.5

Multiple Choice

Solve for x.

• 4

• 6

• 10

• 7

Multiple Choice

Solve for x.

• 3

• 6

• 7

• 5

Poll

Aftr this lesson, this is how I feel about this topic:

• Excited or Happy 😀

• Overwhelmed or Confused 😵

• Sad or Disappointed 😭

• Angry or Frustrated 😡

• Meh (Not Great, Not Bad) 😐