Similar figures have the same shape with corresponding angles equal and corresponding sides proportional.
One figure is an enlarged or reduced copy of another—same shape, same angles, but possibly different size.
Showing a random 20 of 50 problems.
Example 1
hard
A photo is enlarged so that the new area is 2.25 times the old. By what factor does each dimension grow?
Example 2
easy
Two similar triangles have side ratio 3:5. Find the perimeter ratio.
Example 3
easy
What does it mean for two figures to be similar?
Example 4
medium
Two similar cans have volumes 8 L and 27 L. Find the ratio of their heights.
Example 5
medium
Two similar cylinders have radii 3 and 5. Find the ratio of their lateral surface areas.
Example 6
medium
A photograph is enlarged so that the new perimeter is 3 times the old. By what factor does the area grow?
Example 7
easy
Two similar figures have side ratio 2:3. What is the ratio of their areas?
Example 8
easy
Triangle PQR∼ Triangle STU. PQ=4, ST=6, QR=7. Find TU.Triangle PQR (PQ = 4, QR = 7); find TU in similar triangle STU where ST = 6
Example 9
medium
In similar figures, a 6 cm side corresponds to a 9 cm side. A second side in the small figure is 8 cm. Find its match.Small similar figure (sides 6 cm and 8 cm); corresponding large sides are 9 cm and 12 cm
Example 10
challenge
Why does a baby animal have proportionally larger surface area relative to its volume than an adult, and why does this matter for heat loss?
Example 11
easy
A figure is similar to another with scale factor 1/2. If the original perimeter is 24, find the new perimeter.Original rectangle (perimeter = 2×8 + 2×4 = 24); scale factor ½ gives new perimeter = 12
Example 12
easy
In similar figures, corresponding angles are ____.
Example 13
easy
Are all squares similar?
Example 14
medium
Two similar rectangles have areas 48 and 108. Find the linear scale factor (large to small).
Example 15
easy
Two similar triangles have corresponding sides 4 and 10. Find the scale factor (large to small).
Example 16
medium
A model car is built at scale 1:24 to a real car. The real car is 4,800 mm long. Find the model's length.
Example 17
hard
A small statue is similar to a big statue. The big one is 3 times as tall and weighs 135 kg. Estimate the small statue's weight assuming same density.
Example 18
hard
Triangle ABC has AB=6,BC=8,CA=10. A similar triangle has its longest side equal to 25. Find the perimeter of the similar triangle.
Example 19
medium
Triangle ABC∼ Triangle DEF with AB=5, DE=20. If AC=8, find DF.
Example 20
challenge
A photograph 4×6 is enlarged so its area becomes 9 times larger. Find the new dimensions.Original 4 × 6 photo; area ×9 means linear ×3, giving enlarged dimensions 12 × 18