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Warm-up

Warm-up. Fill in the blank with always , sometimes , or never . Explain your answer. A bisector of a segment is ______ a line. A ray ______ has a midpoint. 3. Congruent segments ______ have equal lengths. 4. If B is between A and C , then AB ________ equals BC. R. 1. S. T.

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Warm-up

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  1. Warm-up • Fill in the blank with always, sometimes, or never. • Explain your answer. • A bisector of a segment is ______ a line. • A ray ______ has a midpoint. • 3. Congruent segments ______ have equal lengths. • 4. If B is between A and C, then AB ________ equals BC.

  2. R 1 S T M 2 3 O N P Lesson 1-4 Angles angle () – a figure formed by two rays that have the same endpoint. The two rays are called sides of the angle. Their common endpoint is called the vertex. Angle name(s) Sides Vertex

  3. acute angle– an angle with measure between 0 and 90. obtuse angle– an angle with measure between 90 and 180. right angle– an angle with measure 90. straight angle– an angle with measure 180.

  4. Postulate 3 Protractor Postulate On AB in a given plane, choose any point O between A and B. Consider OA and OB and all the rays that can be drawn from O on one side of AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: a. OA is paired with 0, and OB with 180. b. If OP is paired with x, and OQ with y, then POQ = |x – y|. P x Q y A O B

  5. Use a protractor to measure each angle to the nearest degree. Then,write three names for each angle.

  6. C B O A If AOC is a straight angle and B is any point not on AC,then B O A C Postulate 4Angle Addition Postulate If point B lies in the interior of AOC,then mAOB + mBOC = mAOC . mAOB + mBOC = 180 .

  7. HOMEWORK#4 page 20 CLE 28-33 all page 21 WE 1-22 all, 26-28 all

  8. B 3 2 4 1 9 8 7 6 5 D C A E Warm-up 1. Name the vertex of 3.2. Name a right angle. State another name for each angle. 3.1 4. BDC5. 3 6. DBC 7. 7 8. 2 9. AEB10. 5

  9. B 35 35 A Lesson 1-4 Angles (continued) congruent angles– angles that have equal measures. congruence marks If mA = mB, then A  B.

  10. 1 3 4 2 3 1 2 4 adjacent angles (adj. s)– two angles in a plane that have a common vertex and a common side but no common interior points. 1 and 2 are adjacent angles. 3 and 4 are NOT adjacent angles.

  11. M O N P If NO bisects MNP, then ___________ bisector of an angle– the ray that divides the angle into two congruent adjacent angles. MNO  ONP.

  12. 2 3 1 O A D Ex. 1) Find each angle measure, given the diagram and information below. Given: m1 = 5x, m2 = (x + 40), and m3 = (x2 – 20)

  13. Ex. 2) Given that AM bisects LAR and AS bisects MAR, find mLAR using the given information. Given:mRAM = (5x – 7), and mMAS = (x + 3)

  14. HOMEWORK#5 page 22 29-36 all Read pages 22-23 and complete the outline of Lesson 1-5, including allvocabulary, postulates and theorems (but NOT the warm-up, examples, or cool-down.

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