Similar Figures
What does it mean if two shapes are similar?
They have equal corresponding angles and sides in proportion (same scale factor)
Write the formula for scale factor.
Scale Factor = New Length ÷ Original Length
Write the ratio of 2 red pens to 4 blue pens in colon form.
2 : 4
Why do architects use scale drawings?
Real objects are too large to draw full size but proportions stay accurate
A student adds instead of multiplies when enlarging a shape. Is this correct?
No — you must multiply by the scale factor
Name two tests that can prove triangles are similar.
AAA, SSS, ASA or SAS
A side increases from 6 cm to 18 cm. What is the scale factor?
18 ÷ 6 = 3
Simplify the ratio 12 : 6.
2 : 1
If the scale is 1 cm : 5 m, what does this mean in words?
1 cm on the drawing represents 5 m in real life
Why is adding 3 to each side when the scale factor is 3 wrong?
Scale factor means multiply, not increase by a fixed amount
If two triangles both have angles 30°, 60° and 90°, are they similar? Why?
Yes — same angles means AAA similarity
A shape is reduced by a scale factor of ½. If the original side was 12 cm, what is the new length?
12 × ½ = 6 cm
If a recipe for 8 people is doubled to serve 16, what happens to all ingredients?
They are multiplied by 2
If a wall measures 4 cm on a scale of 1 cm : 10 m, what is the real length?
40 m
A student multiplies one triangle side by 3 instead of the scale factor of 2. What’s the mistake?
They used the wrong multiplier — all sides must use the same scale factor
Two shapes have equal angles but their sides are not proportional. Are they similar?
No — sides must be in the same ratio as well
If the scale factor is 3 and a side is 4 cm, what is the new scaled side?
4 × 3 = 12 cm
On a map, 1 cm represents 10 km. A road is 6 cm long. How long is it in real life?
6 × 10 = 60 km
A bedroom is drawn 6 cm long at 1 cm : 5 m. Find the real length.
30 m
Why is treating a rectangle as having four equal sides wrong?
Rectangles have pairs of equal sides, not all the same
Explain what “corresponding sides” means.
Sides in the same position in each shape (top matches top, left matches left, etc.)
A model side is 8 cm. The real object is 32 cm. Find the scale factor.
32 ÷ 8 = 4
If 5 cm represents 50 km, how far does 1 cm represent?
10 km (divide both by 5)
Explain how proportional reasoning helps in scale drawings.
You multiply or divide all measurements by the same factor to keep proportions the same
Why must every side be scaled by the same factor?
To keep the shape proportional and similar