Vertical Angles

Vertical Angles Example:

∠2 and ∠4 are vertical angles

∠1 and ∠3 are vertical angles

Vertical Angles Definition:

Each of the pairs of opposite angles made by two intersecting lines

Properties:

Vertical angles are always congruent

Vertical angles always have the same measure

Vertical angles are opposite each other at the same intersection point.

Vertical angles are never adjacent.

Vertical angles are non-overlapping.

Vertical angles are only supplementary when the intersecting lines that form them are perpendicular.

All 4 Vertical angles formed by intersecting lines have an angle sum of 360°.

Vertical angles cross at a single point.

Vertical angles share a common vertex.

Vertical Angles Proof Number 1:

Two-Column Proof

Given: a || b and t with transversal t

Prove: ∠2 and ∠4 are congruent

Statement	Reason
a || b and t with transversal t	Given
∠1 + ∠2 = 180°	Linear pair of angles
∠1 + ∠4 = 180°	Linear pair of angles
∠1 + ∠2 = ∠1 + ∠4	Transitive Property
∠2 = ∠4	Equality Property

Vertical Angles Proof Number 2:

Two-Column Proof

Given: a || b and t with transversal t

Prove: ∠1 and ∠3 are congruent

Statement	Reason
a || b and t with transversal t	Given
∠2 + ∠1 = 180°	Linear pair of angles
∠2 + ∠3 = 180°	Linear pair of angles
∠2 + ∠1 = ∠2 + ∠3	Transitive Property
∠1 = ∠3	Equality Property

Final Answer

Vertical angles are always congruent
Vertical angles always have the same measure

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