What You Need to Know

Key Concept Diagram

State what is given, what is to be proved, and list numbered steps with reasons

Common reasons: corresponding angles (parallel lines), vertically opposite angles, angle sum of triangle

Congruence proofs use SSS, SAS, AAS, or RHS tests

Similarity proofs show shape ratios are equal with matching angles

Key Vocabulary

Theorem

A mathematical statement that has been proven to be true

Congruent

Identical in shape and size; corresponding sides and angles are equal

Similar

Same shape but different size; corresponding angles equal, sides in proportion

Corollary

A theorem that follows easily from a previously proven theorem

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

In a proof, what does "vertically opposite angles" justify?

Two angles on a straight line sum to 180 degrees Corresponding angles between parallel lines are supplementary Co-interior angles between parallel lines are supplementary Two angles formed by intersecting lines at the crossing point are equal

Question 2

Which test CANNOT prove two triangles are congruent?

SSA SAS SSS AAS

Question 3

To prove two triangles are similar, you need to show:

All three sides are equal Two pairs of corresponding angles are equal One pair of equal angles All three sides are in the same ratio and one angle is equal

Formal Geometric Proofs