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Understanding Adjacent, Complementary, and Supplementary Angles in Geometry

This lesson explores pairs of angles in geometry, focusing on adjacent, complementary, supplementary, and vertical angles. Adjacent angles share a common vertex and side but do not overlap. Complementary angles add up to 90˚, while supplementary angles sum to 180˚, often forming linear pairs. Vertical angles are non-adjacent angles formed by intersecting lines. The lesson provides definitions, examples, and methods to find angle measures through algebraic equations. Key concepts like congruence and key angle relationships are also emphasized.

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Understanding Adjacent, Complementary, and Supplementary Angles in Geometry

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  1. Pairs of Angles Unit 5: Geometry

  2. Adjacent Angles Definition: A pair of angles with a shared vertexand common sidebut 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

  3. 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

  4. 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

  5. Vertical Angles Definition: A pair of angles whose sides form opposite rays. Examples: Vertical angles are non-adjacent angles formed by intersecting lines. Lesson 1-5: Pairs of Angles

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

  7. What’s “Important” in Geometry? 4 things to always look for ! 90˚ 180˚ 360˚ Most of the rules (theorems) and vocabulary of Geometry are based on these 4 things. . . . andCongruence Lesson 1-5: Pairs of Angles

  8. 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

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

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

  11. Algebra and Geometry Common Algebraic Equations used in Geometry: ( ) = ( ) ( ) + ( ) = ( ) ( ) + ( ) = 90˚ ( ) + ( ) = 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

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