Identify complementary, supplementary, vertical, adjacent, and congruent angles

Learning Objectives Identify and define complementary angles. Identify and define supplementary angles. Identify and define vertical angles. Identify and define adjacent angles. Determine if two angles are congruent based on their relationship or given information. Calculate unknown angle measures using the properties of these angle pairs. Distinguish between different types of angle relationships in geometric figures. Ever wonder how architects design buildings with perfect corners, or how pool players aim their shots? 📐 It all comes down to understanding angles! In this lesson, you'll learn to identify and classify different types of angle pairs: complementary, supplementary, vertical, adjacent, and congruent angles. Mastering these concepts is crucial for underst...

TermDefinitionExample AngleA figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex.In $\angle ABC$, point B is the vertex, and rays BA and BC are the sides. VertexThe common endpoint where two rays of an angle meet.For $\angle XYZ$, the point Y is the vertex. Complementary AnglesTwo angles whose measures add up to exactly $90^\circ$.A $30^\circ$ angle and a $60^\circ$ angle are complementary because $30^\circ + 60^\circ = 90^\circ$. Supplementary AnglesTwo angles whose measures add up to exactly $180^\circ$.A $70^\circ$ angle and a $110^\circ$ angle are supplementary because $70^\circ + 110^\circ = 180^\circ$. Vertical AnglesA pair of non-adjacent angles formed by the intersection of two straight lines. They are always congruent.When two li...

Complementary Angles Sum If two angles, $\angle A$ and $\angle B$, are complementary, then $m\angle A + m\angle B = 90^\circ$. Use this rule when you know two angles form a right angle or are stated to be complementary. Supplementary Angles Sum If two angles, $\angle A$ and $\angle B$, are supplementary, then $m\angle A + m\angle B = 180^\circ$. Use this rule when two angles form a straight line or are stated to be supplementary. Vertical Angles Property Vertical angles are congruent. If $\angle 1$ and $\angle 3$ are vertical angles, then $m\angle 1 = m\angle 3$. Use this rule when two straight lines intersect, and you need to find the measure of an angle opposite a known angle.