Angle vocabulary

Learning Objectives Define and identify key angle types and angle pairs, including adjacent, vertical, complementary, and supplementary angles. Identify and name the specific angle pairs formed by a transversal intersecting two lines (alternate interior, alternate exterior, corresponding, consecutive interior). Apply the Angle Addition Postulate to find unknown angle measures. Use the properties of linear pairs and vertical angles to solve for unknown variables and angle measures. Apply theorems about angles formed by parallel lines and a transversal to justify geometric statements and find missing angle measures. Use correct geometric notation for naming angles and expressing their measures. Distinguish between angle congruence (≅) and equality of angle measures (=). Ever...

TermDefinitionExample Linear PairA pair of adjacent angles whose non-common sides are opposite rays. The angles in a linear pair are always supplementary.If ray B→D stands on line A↔C, then ∠ABD and ∠DBC form a linear pair. Their measures add up to 180°. Vertical AnglesA pair of non-adjacent angles formed by the intersection of two lines. Vertical angles are always congruent.When lines 'l' and 'm' intersect at point P, the angles opposite each other are vertical angles. If ∠1 and ∠3 are opposite, then ∠1 ≅ ∠3. TransversalA line that intersects two or more coplanar lines at distinct points.In a diagram with lines 'a' and 'b', a third line 't' that crosses both 'a' and 'b' is a transversal. Alternate Interior AnglesA pair...

Angle Addition Postulate If point B lies in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC. Use this postulate to find the measure of a larger angle when you know its parts, or to find a part when you know the whole and the other part. It's often used in problems with algebraic expressions. Linear Pair Postulate If ∠1 and ∠2 form a linear pair, then m∠1 + m∠2 = 180°. This rule states that angles forming a straight line are supplementary. It is fundamental for finding unknown angles on a straight line. Vertical Angles Theorem If ∠1 and ∠3 are vertical angles, then ∠1 ≅ ∠3, which implies m∠1 = m∠3. This theorem provides a powerful shortcut for finding the measure of an angle when you know the measure of the angle directly opposite it at an intersection.