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Warm Up

Warm Up. x = 14. Solve. x = 9. x = 2. Geometry Vocabulary. Point. An exact position or location in a given plane. Point A or Point B. Line. The set of points between points A and B in a plane and the infinite number of points that continue beyond the points. Written as. Line Segment.

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Warm Up

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  1. Warm Up x = 14 Solve. x = 9 x = 2

  2. Geometry Vocabulary

  3. Point An exact position or location in a given plane. Point A or Point B

  4. Line The set of points between points A and B in a plane and the infinite number of points that continue beyond the points. Written as

  5. Line Segment A line with two endpoints. Written as

  6. Ray A line that starts at A, goes through B, and continues on. Written as

  7. Plane A flat, two-dimensional surface that extends infinitely far.

  8. Angle Formed by 2 rays coming together at a common point (Vertex) The angle is

  9. Types of Angles

  10. Acute Angle An angle measuring less than 90° but greater than 0°.

  11. Right Angle An angle that measures 90°.

  12. Obtuse Angle An angle measuring greater than 90° but less than 180°.

  13. Straight Angle An angle measuring exactly180°. A line.

  14. Name this angle 4 different ways. CAT TAC  A C 2 A 2  T 

  15. Name the ways can you name 3? MHA and AHM Name the ways can you name 4? AHT and THA Name the ways can you name MHT? THM M  A  3   4 T H

  16. Complementary Angles Solve for x if the following 2 angles are complementary. x 76 Equation: ____ + ____ = 90 14 Two angles that add up to 90.

  17. Solve for x. 2x + 23 x + 13 x = 18

  18. One of two complementary angles is 16 degrees less than its complement. Find the measure of both angles. 1st Angle: 2nd Angle: x = 53 One angle is 53 and the other is 37.

  19. Supplementary Angles Solve for x if the following 2 angles are supplementary. x 82 Equation: ____ + ____ = 180 Two angles that add up to 180. 98

  20. One of two supplementary angles is 46 degrees more than its supplement. Find the measure of both angles. 1st Angle: 2nd Angle: x = 67 One angle is 67 and the other is 113.

  21. Angle Bisector Solve for x. Cuts an angle into TWO congruent angles 2x + 40 5x + 16 x = 8

  22. Vertical Angles Solve for x. x 76 Equation: ______ = ______ Two angles that share a common vertex and their sides form two pairs of opposite rays. 76

  23. Solve for x. (3x + 23)° (4x + 18)° x = 5

  24. Linear Pair Solve for x. x 62 Two angles that are side-by-side, share a common vertex, share a common ray, & create a straight line. Equation: ____ + ____ = 180 118

  25. Solve for x. x + 104 x x = 38

  26. Solve for x. x = 23

  27. Angle Addition Postulate If B lies on the interior of ÐAOC, then mÐAOB+ mÐBOC= mÐAOC. B A mÐAOC = 115° 50° C 65° O

  28. D Example 1: Example 2: G 114° K 134° 46° A B C 95° 19° This is a special example, because the two adjacent angles together create a straight angle. Predict what mÐABD+ mÐDBCequals. ÐABC is a straight angle, therefore mÐABC= 180. mÐABD+ mÐDBC= mÐABC mÐABD+ mÐDBC= 180 So, if mÐABD= 134, then mÐDBC= ______ H J Given: mÐGHK= 95 mÐGHJ= 114. Find: mÐKHJ. The Angle Addition Postulate tells us: mÐGHK+ mÐKHJ= mÐGHJ 95 + mÐKHJ= 114 mÐKHJ= 19. Plug in what you know. 46 Solve.

  29. Given: mÐRSV= x + 5 mÐVST= 3x - 9 mÐRST= 68 Find x. R V Extension: Now that you know x = 18, find mÐRSVand mÐVST. mÐRSV= x + 5 mÐRSV= 18 + 5 = 23 mÐVST= 3x - 9 mÐVST= 3(18) – 9 = 45 Check: mÐRSV+ mÐVST= mÐRST 23+ 45 =68 S T Set up an equation using the Angle Addition Postulate. mÐRSV+ mÐVST= mÐRST x + 5 + 3x – 9 = 68 4x- 4 = 68 4x = 72 x = 18 Plug in what you know. Solve.

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