Ratios · Scaling & similar figures · 5.3

Similar figures.

Similar figures are the same shape, scaled. Their corresponding sides are proportional — the ratio between matching sides is constant. That ratio is the scale factor.

01 / THE IDEA

See it work.

Similar figures

Same shape, scaled.

Corresponding sides are proportional — so the ratio is the same.

46
→
812

4/6 = 8/12 → the missing side is 12.

Watch the method

Similar figures

Matching sides keep the same ratio.

1 / 2
46=8x\frac{4}{6} = \frac{8}{x}
1

Set up the proportion

Corresponding sides of similar figures are proportional.

46=8x\frac{4}{6} = \frac{8}{x}
2

Cross-multiply & solve

Solve for the missing side.

x=12x = 12
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 40.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Same shape, scaled

Corresponding sides of similar figures form equal ratios; that common ratio is the scale factor.

Why it works

Every side scales by the same factor.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Two similar figures: a 3-side matches a 12-side. The matching figure has a 6-side — find the other side.

1

Set up the proportion

Corresponding sides of similar figures are proportional. 3/12 = 6/x

2

Cross-multiply & solve

Solve for the missing side. x = 24

EX 2medium

Two similar figures: a 4-side matches a 8-side. The matching figure has a 16-side — find the other side.

1

Set up the proportion

Corresponding sides of similar figures are proportional. 4/8 = 16/x

2

Cross-multiply & solve

Solve for the missing side. x = 32

EX 3hard

Two similar figures: a 5-side matches a 10-side. The matching figure has a 15-side — find the other side.

1

Set up the proportion

Corresponding sides of similar figures are proportional. 5/10 = 15/x

2

Cross-multiply & solve

Solve for the missing side. x = 30

04 / COMMON TRAPS

Where students slip.

Trap

Comparing non-corresponding sides.

Fix

Match each side to its partner.

Trap

Assuming equal differences.

Fix

Sides scale by a ratio, not a difference.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Two similar figures: a 2-side matches a 6-side. The matching figure has a 4-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
C2

Two similar figures: a 3-side matches a 12-side. The matching figure has a 9-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
C3

Two similar figures: a 3-side matches a 6-side. The matching figure has a 6-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
C4

Two similar figures: a 3-side matches a 9-side. The matching figure has a 6-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
Apply

Apply (4)

A1

Two similar figures: a 5-side matches a 15-side. The matching figure has a 20-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
A2

Two similar figures: a 5-side matches a 15-side. The matching figure has a 10-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
A3

Two similar figures: a 3-side matches a 9-side. The matching figure has a 6-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
A4

Two similar figures: a 4-side matches a 16-side. The matching figure has a 16-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
Extension

Extension (4)

E1

Two similar figures: a 2-side matches a 6-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
E2

Two similar figures: a 2-side matches a 4-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
E3

Two similar figures: a 2-side matches a 8-side. The matching figure has a 6-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.
E4

Two similar figures: a 3-side matches a 12-side. The matching figure has a 9-side — find the other side.

Need a hint?
  • Match corresponding sides.
  • Set up equal ratios.