Similar figures have equal angles and corresponding sides in a constant ratio.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Finding a missing side
Set up the ratio of corresponding sides and solve.
Match them correctly
Pair sides that sit between the same two angles, not the ones that look alike.
Areas
If sides are in ratio k, areas are in ratio k².
Both conditions define similarity
Similar figures have equal corresponding angles and proportional corresponding sides. For triangles either condition implies the other; for general polygons both must be checked independently.
Setting up the proportion
Write the ratio consistently: new over old for every pair, or old over new for every pair. Mixing directions within a single proportion is the standard error, and it produces an answer that is the reciprocal of the truth.
Areas and volumes again
Side ratio k gives area ratio k² and volume ratio k³. Problems that give an area ratio and ask for a side ratio require taking a square root, which is the step most often forgotten.
Measuring the unreachable
Shadow lengths, mirrors on the ground and sighting devices all create similar triangles that let you compute the height of something you cannot climb. This is one of the oldest practical uses of geometry and it still works.
Step 2: Try It Yourself
Tap and try it out.
Before: 6
After: 9
The factor is more than 1, so the bar got longer.
Step 3: Watch an Example
One step at a time.
Watch Kofi Find a Missing Side
Two similar triangles: 4 corresponds to 6, and 10 corresponds to x.
- Step 1
The scale factor is 6 ÷ 4 = 1.5.
Step 4: Your Turn
Practice makes it stick.
The Factor
Problem 1 of 2
4 corresponds to 12. What is the scale factor?
The Missing Side
Problem 2 of 2
Same factor. 7 corresponds to what?
Scale and Compare
1 of 8
5 corresponds to 20. Scale factor?
2 of 8
Factor 4. 3 corresponds to what?
3 of 8
Sides in ratio 2. What is the area ratio?
4 of 8
Sides in ratio 3. What is the area ratio?
5 of 8
Do similar figures have equal angles? 1 for yes, 0 for no.
6 of 8
Do similar figures have equal sides? 1 for yes, 0 for no.
7 of 8
Areas in ratio 25. What is the side ratio?
8 of 8
Factor 0.5. Is the image smaller? 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
Sides in ratio 4. Area ratio?
What You Learned
- Similar figures have equal angles and sides in a constant ratio.
- Match corresponding sides by their position, not their appearance.
- Sides in ratio k put areas in ratio k².