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1. Name a plane. 2. Name a line. 3. Name a ray. 4. Name a point. 5. Name three collinear points.

Warm Up. 6. Name four coplanar points. 7. Name a segment. 8. Do points T and Q lie on the same line? 9. Plane RYT Ç plane EWTR is _______. 10. How many planes does point S lie on?. 1. Name a plane. 2. Name a line. 3. Name a ray. 4. Name a point. 5. Name three collinear points.

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1. Name a plane. 2. Name a line. 3. Name a ray. 4. Name a point. 5. Name three collinear points.

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  1. Warm Up 6. Name four coplanar points. 7. Name a segment. 8. Do points T and Q lie on the same line? 9. Plane RYT Ç plane EWTR is _______. 10. How many planes does point S lie on? 1. Name a plane. 2. Name a line. 3. Name a ray. 4. Name a point. 5. Name three collinear points.

  2. Homework Answers • pg. 15 • True • False • True • True • False • True • False • True • True • False • True • False • False • True • pg. 16 • 33) x = 6 • 34) x = 11 • 35) x = 3 • 36) x = 7 • y = 6 • y = 7 • z = 8 • GE = 10, EH = 10 • E is the midpoint of GH • z = 5 • GE = 5, EH = 6 • E is not the midpoint of GH

  3. Section 1-4 Angles In this section we will discuss the proper notation of angles, specific classifications of angles, and the properties of angle bisectors and the Angle Addition Postulate.

  4. Angles Angle – the figure formed by two rays that have the same endpoint. Sides C The two rays are called the sides; the shared endpoint is called the vertex. Vertex T A

  5. We name an angle using three letters and theÐ symbol. Acceptable: ÐCAT ÐTAC Unacceptable: ÐACT ÐTCA C A T Order Matters!! The vertex must be the letter in the middle!

  6. B Sometimes using only one letter may not be specific enough, because it may refer to more than one angle. IF THERE IS ANY DOUBT, USE THREE LETTERS! Alternative Notation You can name an angle just with the vertex. This angle could beÐA. C A T ÐCAB ÐCAT ÐBAT

  7. We also may name angles with numbers. C ÐCAB is Ð1 ÐBAT is Ð2 B 1 T A 2

  8. Measuring Angles We measure angles using a protractor. The units for angle measurement is degrees. Symbol for Degree: Measure of Angle: mÐABC 70°

  9. Measure Angles #1-9 using your protractor. Estimate to the nearest degree.

  10. Classifying Angles An angle measuring between 90°and 180°. An angle measuring between 0°and 90°. An angle measuring exactly 90°. An angle measuring exactly 180°. Obtuse Angle Acute Angle Right Angle Straight Angle A pair of opposite rays creates a straight angle.

  11. T B C A D H E Angle Interior Any points that lie inside the angle.

  12. Congruent Angles M Z P T 120° 120° A I Recall the Definition of Congruent: Figures that are the same shape and size. Congruent Angles – angles that have equal measures. Remember: Figures can be congruent; measures can be equal. ÐMAT @ÐZIP mÐMAT = mÐZIP

  13. Adjacent Angles C B T A Definition: two angles in a plane that have a common vertex and a common side but no common interior points. ÐCAB and ÐBAT are adjacent angles. ÐCAT and ÐBAT are NOT adjacent because they share interior points.

  14. Angle Bisector is an angle bisector. 60° 60° Definition: a ray that divides an angle into two congruent adjacent angles. ÐXWY @ÐYWZ Y X Z W

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

  16. mÐBQC = x - 7 mÐCQD = 2x - 1 mÐBQD = 2x + 34 Find x, mÐBQC, mÐCQD, mÐBQD. C B Q D x = 42 mÐBQC + mÐCQD = mÐBQD mÐBQC = 35 x – 7 + 2x – 1 = 2x + 34 mÐCQD = 83 3x – 8 = 2x + 34 mÐBQD = 118 x – 8 = 34

  17. Home Work Pg.21 #1 – 18, 29 – 34 Update Postulate Section – Angle Addition Postulate

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