WELCOME 2 2 Special Angles Last Nights Homework

WELCOME 2. 2: Special Angles Last Night’s Homework: 2. 1 Handout Tonight’s Homework: 2. 2 Handout

Warm Up

Homework Questions

Chapter 2 Section 2

Parts of an Angle An angle consists of two different rays that share an common initial point B Vertex Sides A C “ ∠BAC, ∠CAB, or ∠ A ”

Interior / Exterior Interior: Points that sit between the sides of an angle Exterior: Points that sit outside of the angle sides B A C

Types of Angles A Acute 0° < m ∠ A < 90 ° A Obtuse 90° < m ∠ A < 180 ° A Right m ∠ A = 90 ° A Straight m ∠ A = 180 °

Adjacent Angles are adjacent if they share a vertex & side, but no interior points A B O C “angles ∠AOB & ∠ BOC are adjacent”

Supplementary Two angles are Supplementary if the sum of their measure is 180° “∠ 5 is the supplement of ∠ 6” “∠ 7 is the supplement of ∠ 8”

Example:

Example:

Complementary Two angles are Complementary if the sum of their measure is 90° “∠ 1 is the complement of ∠ 2” “∠ 4 is the complement of ∠ 3”

Example:

Example: Find x and the measure of each angle.

Linear Pair Two adjacent angles form a linear pair if their non common side form a line 5 6 ∠ 5 and ∠ 6 are a linear pair The sum of the measures for a linear pair = 180° m ∠ 5 + m ∠ 6 = 180°

Vertical Angles Two angles are called vertical angles if their sides form two pairs of opposite rays 4 1 3 2 ∠ 1 and ∠ 3 are vertical angles ∠ 2 and ∠ 4 are vertical angles Vertical angles are Congruent ∠ 1 ∠ 3 ∠ 2 ∠ 4

Linear Pair Postulate If two angles form a linear pair, then the angles are supplementary. B 85⁰ ? D A C

Segment Addition Postulate Given, AB BC A B AC If B sits between A & C , C

Angle Addition Postulate Given RST, R P S T If P is in the interior of m RSP + RST, then… m PST = m RST