Similarity Flashcards

All 6 cards in this deck

What does it mean for two shapes to be mathematically similar?

One is an enlargement of the other: corresponding angles are equal and all corresponding sides are in the same ratio.

What is the scale factor between two similar shapes?

The number every length is multiplied by: a length on the second shape $\div$ the corresponding length on the first.

Two triangles have the same three angles. Are they mathematically similar?

Yes. Equal corresponding angles is enough for triangles to be similar.

True or false? All rectangles are mathematically similar to each other.

False. Their angles match, but the sides need not be in the same ratio.

True or false? In two similar shapes the corresponding angles are equal.

True. Enlargement changes lengths but not angles.

What are the steps to show two triangles are mathematically similar?

e.g. sides $3, 4, 5$ cm and $7.5, 10, 12.5$ cm

1. Pair up corresponding sides (smallest with smallest, etc.)
2. Divide each pair: $7.5\div3=2.5$, $10\div4=2.5$, $12.5\div5=2.5$
3. State all sides are enlarged by the same scale factor, so the triangles are similar.