Starter: Similarity, Congruence, and Scale (Year 10 PGM)

Flashcards covering complementary/supplementary angles, congruence vs similarity, similarity notation and tests (AAA, SSS, SAS, RHS), scale factor, and related concepts from the notes.

What is a complementary angle?

Two angles whose measures add up to 90 degrees.

What is a supplementary angle?

Two angles whose measures add up to 180 degrees.

What is the symbol for congruence?

≅ (congruent to).

What are the four congruence tests for triangles?

SSS, SAS, AAS, and RHS.

What is a similarity between triangles?

Triangles that have the same shape but may differ in size; they can be rotated and/or reflected and overlayed.

How is similarity written between triangles?

△ABC ∼ △DEF (also written △ABC III △DEF).

What does the AAA (angle–angle–angle) similarity test state?

All three corresponding angles are equal.

What does the SSS similarity test state?

Three pairs of corresponding sides are in the same ratio.

What does the SAS similarity test state?

Two pairs of corresponding sides are in the same ratio and the included angle is equal.

What does the RHS similarity test state?

In right-angled triangles, the ratio of the hypotenuse to a corresponding side is equal.

What are the conditions for two triangles to be similar?

They have equal corresponding angles and proportional corresponding sides.

How do congruent and similar triangles differ?

Congruent triangles are identical in size and shape; similar triangles have the same shape but may differ in size.

What is the similarity notation and how is it read?

|||, read as 'is similar to' (e.g., △ABC ∼ △DEF or △ABC III △DEF).

What is a scale factor?

The ratio of a length in a larger figure to the corresponding length in a smaller figure.

How do you compute the scale factor from two similar figures?

Scale Factor = Large Object / Small Object.

Do similar figures have the same size?

No. They have the same shape, but sizes may differ; corresponding sides are in a constant ratio.

How many measures define a triangle, and what are they?

Six measures: three sides and three angles; not all are needed to prove congruence or similarity.

Can similar triangles be rotated or reflected to show similarity?

Yes; rotation and/or reflection can be used to overlay triangles and demonstrate similarity.