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Geometry Notes

Geometry Notes. Lesson 1.3A – Angles LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics and complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines. Angle.

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Geometry Notes

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  1. Geometry Notes Lesson 1.3A – Angles LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics and complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines.

  2. Angle • The figure formed by two rays with a common endpoint. side vertex side

  3. Three ways to name an angle: • The vertex (only when there is one angle at the vertex) • Three letters (vertex is always the middle letter) • A number

  4. A B D C Angle Addition Postulate • If D is in the interior of ABC, then m ABD + m DBC = m ABC

  5. A B D C Example… Given m ABD = 45° m DBC = 32° m ABC = _____________

  6. S R 25° 50° T 43° Q P Now You Try… • m SQT = _________ • m PQR = _________ • m SQP = _________

  7. X Y O Z W Types of Angles • Vertical Angles – nonadjacent angles formed by two intersecting lines • Name a pair of vertical angles. • Look at the size (measurement) of one pair of vertical angles. What might you guess about their measurements?

  8. A C E O D F B Now You Try… Name a second angle in each pair of vertical angles. • EOD • BOC • EOB

  9. D 105O 75O C Types of Angles (cont.) • Supplementary Angles – two angles, whose sum of their measures equals180° Angles C and D are supplementary.

  10. xo 120o Example… x =

  11. 50O A 40o B Types of Angles (cont.) • Complementary Angles – two angles, whose sum of their measures equals 90° Angles A and B are complementary.

  12. yo 25o Example. . . y =

  13. K L P M N Example . . . Given: KLM is a right angle. • If m KLP = 57°, find m MLP. • If m MLP = 69°, find m KLP. • If m NPM = 120°, find m MPL. • If m KPL = 130°, find m KPN

  14. B C E D A Now you try. . . Given: BAD is a right angle. • If m BAE = 74°, find m EAD. • If m EAD = 36°, find m BAE. • If m CED = 71°, find m CEB. • If m AED = 117°, find m BEA.

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