Similarity Flashcards

All 6 cards in this deck

What does it mean for two shapes to be similar?

Corresponding angles are equal and corresponding sides are all in the same ratio — one is an enlargement of the other.

What is the simplest condition that proves two triangles are similar?

AA — two pairs of corresponding angles are equal (the third pair is then equal too).

In two similar triangles, how do you tell which sides correspond?

Corresponding sides are opposite equal angles (they join the same pairs of matching vertices).

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

False. Their angles match but the ratios of the sides need not be equal, e.g. $2\times3$ and $2\times5$.

True or false? AAA (three equal angles) proves two triangles are congruent.

False. Equal angles only prove the triangles are similar; the sides may be different sizes.

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

e.g. $\triangle ABC$ and $\triangle AED$, where $BC$ is parallel to $ED$

1. Find a pair of equal angles with a reason: $\angle A$ is common.
2. Find a second pair with a reason: $\angle ABC = \angle AED$ (corresponding angles, $BC \parallel ED$).
3. Conclude: the triangles are similar (AA).