Lesson 1-5: Pairs of Angles

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Presentation transcript:

Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Adjacent Angles Definition: A pair of angles with a shared vertex and common side but do not have overlapping interiors. Examples: 1 and 2 are adjacent. 3 and 4 are not. 1 and ADC are not adjacent. 4 3 Adjacent Angles( a common side ) Non-Adjacent Angles Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Complementary Angles Definition: A pair of angles whose sum is 90˚ Examples: Adjacent Angles ( a common side ) Non-Adjacent Angles Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Supplementary Angles Definition: A pair of angles whose sum is 180˚ Examples: Adjacent supplementary angles are also called “Linear Pair.” Non-Adjacent Angles Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Vertical Angles Definition: A pair of angles whose sides form opposite rays. Examples: ***Vertical Angles are ALWAYS congruent!!!*** Lesson 1-5: Pairs of Angles

Theorem: Vertical Angles are = ~ Given: The diagram Prove: Statements Reasons 1. 1. Definition: Linear Pair 2. 2. Property: Substitution 3. 3. Property: Subtraction 4. 4. Definition: Congruence Lesson 1-5: Pairs of Angles

Example: If m4 = 67º, find the measures of all other angles. Step 1: Mark the figure with given info. Step 2: Write an equation. 67º Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Example: If m1 = 23 º and m2 = 32 º, find the measures of all other angles. Answers: Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Example: If m1 = 44º, m7 = 65º find the measures of all other angles. Answers: Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Algebra and Geometry Common Algebraic Equations used in Geometry: (Part 1) = (Part 2) (Part 1) + (Part 2) = (Whole) (Part 1) + (Part 2) = 90˚ (Part 1) + (Part 2) = 180˚ If the problem you’re working on has a variable (x), then consider using one of these equations. Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Example 4: If m<3 = 35x – 2, m<6 = 32x + 7, and m<4 = 7x –1, find x and the measure of each missing angle. Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles Perpendicular Lines When 2 lines are perpendicular, they form 4 right angles. The symbol for perpendicular lines is: Therefore, A D C B Lesson 1-5: Pairs of Angles

Lesson 1-5: Pairs of Angles