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OTCQ The Straight Angle:

OTCQ The Straight Angle: The degree measure of a straight angle is 180 °. Given:  ABC is a straight angle and  ABD = 125 °. What can you conclude about  DBC. D. 125 °. A. B. C. OTCQ # 2 The Straight Angle:

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OTCQ The Straight Angle:

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  1. OTCQ The Straight Angle: The degree measure of a straight angle is 180°. Given:  ABC is a straight angle and  ABD = 125°. What can you conclude about  DBC D 125° A B C

  2. OTCQ # 2 The Straight Angle: The degree measure of a straight angle is 180°. Given:  ABC is a straight angle and  ABD = 125°. What can you conclude about  DBC D 125° 55° A B C

  3. OTCQ # 2 The Straight Angle: The degree measure of a straight angle is 180°. Given:  ABC is a straight angle and  ABD = 125°. What can you conclude about  DBC D 125° 55° A B C VERTEX IS THE MIDDLE LETTER

  4. AIM 4-2 How do we use definitions and postulates in proofs? GRP 7, GPS 2 and GPS 4 Homework: See HWK Sheet

  5. OBJECTIVE 1. SWBAT explain and use properties and postulates in proofs.

  6. Properties of Equality 1) Reflexive: a = a 2) Symmetric: If a = b then b = a. • Transitive: If a = b and b = c, then a = c. • Substitution: If a = b, then a can be replaced by b.

  7. Postulates 1-4 • 1. A straight line segment can be drawn joining any two points. • 2. Any straight line segment can be extended indefinitely in a straight line. • 3. Two lines cannot intersect in more than one point. • 4. One and only one circle can be drawn with any given point as center and the length of any given line segment as the radius.

  8. Postulates 5 -8 • 5. At any given point on a given line, one and only one perpendicular line can be drawn to the line. • 6. From a given point not on a given line, one and only one perpendicular can be drawn to the given line. • 7. For any two distinct points, there is only one positive real number that is the distance between the two points. • 8. The shortest distance between two points is the length of the line segment joining these two points.

  9. Postulates 9- 10 • 9. A line segment has one and only one midpoint. • 10. An angle has one and only one bisector.

  10. Proof practice: given: ABC is a straight angle and BD bisects ABC. Prove BD AC Statements Reasons

  11. D given: ABC is a straight angle and BD bisects ABC. Prove BD AC A C B Statements Reasons 1.  ABC is a straight angle and BD bisects ABC Conclusion: BD AC 1. Given

  12. D given: ABC is a straight angle and BD bisects ABC. Prove BD AC A C B Statements Reasons 1.  ABC is a straight angle and BD bisects ABC. 2.If  ABC is a straight ○ Angle, then m ABC is 180. Conclusion: BD AC 1. Given 2. Straight angle definition.

  13. D given: ABC is a straight angle and BD bisects ABC. Prove BD AC A C B Statements Reasons • 1.  ABC is a straight angle • and BD bisects ABC. • 2.If  ABC is a straight • Angle, then m ABC is • 180° . • If BD bisects a 180° angle, • then each resulting angle • will equal 90° . • Conclusion: BD AC 1. Given 2. Straight angle postulate. 3. Angle Bisector postulate.

  14. D given: ABC is a straight angle and BD bisects ABC. Prove BD AC A C B Statements Reasons 1. Given 2. Straight angle postulate. 3. Angle Bisector postulate. 4. Perpendicular lines definition. • 1.  ABC is a straight angle • and BD bisects ABC. • 2.If  ABC is a straight • Angle, then m ABC is • 180° . • If BD bisects a 180° angle, • then each resulting angle • will equal 90° . • 4. Lines that intersect at a 90° • Angle are perpendicular. • Conclusion: BD AC

  15. 4 1 2 3 Statements Reasons Given: The Diagram Prove: 1  3 + 4

  16. Geometry Test Sample on Postulates Name:_________________Nelson Mandela High School Maximum Value 35: Score = Part 1 Vocabulary: Fill in the missing words in each postulate exactly as presented in class and in Section 4-1. 1 point each. Write clearly. No partial credit. • Two lines cannot _________________________________________________ ____________________________________________________________________ 2. One and only one circle can be drawn with ____________________________________________________________________ ____________________________________________________________________ 3. From a given point not on a given line, ____________________________________________________________________ ____________________________________________________________________ 4. The shortest distance between two points is ________________________________ ____________________________________________________________________. 5. A line segment has one _______________________________________________.

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