Honors Geometry: Reasons for Proofs

Congruency

Congruent segments/angles have equal measure.

Right angle

A right angle = 90°.

Straight angle

A straight angle = 180°.

Obtuse angle

An obtuse angle > 90° and < 180°.

Acute angle

An acute angle < 90°.

Segment bisector

A line/segment/ray that cuts another segment into 2 ≅ parts.

Segment trisector

Two rays/points divide a segment into 3 ≅ parts.

Collinear points

3 pts that lie on the same line.

Midpoint

The point dividing a segment into 2 ≅ parts.

Angle bisector

A ray that divides an angle into 2 ≅ angles.

Angle trisector

Two rays that divide an angle into 3 ≅ angles.

Addition property

If a = b, then a + c = b + c.

Subtraction property

If a = b, then a - c = b - c.

Division property

If a = b and c ≠ 0, then a/c = b/c.

Multiplication property

If a = b, then ac = bc.

Reflexive property

a = a (or segment AB ≅ segment AB).

Transitive property

If a = b and b = c, then a = c.

Distributive property

a(b + c) = ab + ac.

Symmetric property

If a = b, then b = a.

Substitution property

Replace equal quantities.

Segment Addition Postulate

If B is between A and C, then AB + BC = AC.

Angle Addition Postulate

If point D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC.

CLT (Combine Like Terms) / Simplify

Algebra clean-up step.