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Honors Geometry

Honors Geometry. Measuring Segments and Angles. Postulates. RULER POSTULATE. The points of a line can be put into 1 to 1 correspondence with the real numbers so that the distance between any 2 points is the absolute value of the difference of the corresponding numbers. RULER POSTULATE. B. A.

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Honors Geometry

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  1. Honors Geometry Measuring Segments and Angles

  2. Postulates RULER POSTULATE The points of a line can be put into 1 to 1 correspondence with the real numbers so that the distance between any 2 points is the absolute value of the difference of the corresponding numbers.

  3. RULER POSTULATE B A AB = |2 – 5| = 3

  4. Congruent • Same measure • Notation:  • Mark up the picture with the same marks AB  CD A B C D 

  5. Let’s Practice    Q P T Given: PT = 5x + 3 and TQ = 7x – 9 Find: PT. x = 6, PT = 33 Answers

  6. Postulates SEGMENT ADDITION POSTULATE If 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC.

  7. Let’s Practice    T D S Given: DT = 60 and DS = 2x – 8 and ST = 3x – 12 Find: x, DS, & ST. Answers x = 16, DS = 24, ST = 36

  8. Let’s Practice    G E F Given: EG = 100 and EF= 4x – 20 and FG = 2x + 30 Find: x, EF, & FG. Answers x = 15, EF = 40, FG = 60

  9. Midpoint • A point that divides a segment into two congruent parts. • A line, a ray, or a segment can bisect another segment.

  10. Bisect • Cut through at the midpoint • A line, a ray, or a segment can bisect another segment.

  11. Trisect • Cut into three equal parts • A line, a ray, or a segment can trisect another segment.

  12. Let’s Practice B A C    Given OC bisects AB, AC = 2x + 1and CB = 3x - 4 Find: AC, CB, & AB. O  x = 5, AC = 11, CB = 11, AB = 22 Answers

  13. Postulates PROTRACTOR POSTULATE Let OA and OB be opposite rays in a plane. OA, OB, and all rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers 0 to 180 so that OA is paired with 0 and OB is paired with 180. If OC is paired with x and OD is paired with y, then mCOD = |x – y|.

  14. PROTRACTOR POSTULATE  D  C    A B O mCOD = |x – y| = |50 – 120| = 70

  15. Types of Angles

  16. Active Inspire Protractor Demonstration

  17. Postulates ANGLE ADDITION POSTULATE If point B is in the interior of AOC, then mAOB + mBOC = mAOC. IfAOC is a straight angle, then mAOB + mBOC = 180.

  18. Let’s Practice  W T   S  R Given: mRST = 50 and mRSW = 125. Find: mTSW mTSW = 75 Answers

  19. Let’s Practice  G    D E F Given: DEF is a straight angle and mDEG = 145. Find: mGEF mGEF = 35 Answers

  20. Angles and the Clock Estimate the measure of the angle formed by the hands of a clock at: 6:00 5:20 4:40

  21. Let’s Practice Q P V N M Given: mMQV = 90 and mVQP = 35. Find: mMQP mMQP = 125 Answers

  22. Let’s Practice Q P V N M Given: mMVQ = 55 Find: mQVP mQVP = 125 Answers

  23. Let’s Practice Q P V N M Judging by appearance, name two obtuse angles. Judging by appearance, name two acute angles.

  24. Let’s Practice A B C O D Given: mAOC = 7x – 2,mAOB = 2x + 8 and mBOC = 3x + 14. Find: x x = 12 Answers

  25. Let’s Practice A B C O D Given: mAOB = 28 ,mBOC = 3x – 2 and mAOD = 6x. Find: x Answers x = 18

  26. Median of a Triangle • The segment joining the midpoint of a side to the opposite vertex.

  27. Challenge C is the midpoint of AB. D is the midpoint of AC. E is the midpoint of AD. F is the midpoint of ED. G is the midpoint of EF. H is the midpoint of DB. If DC = 16, find GH.

  28. GH = GF + FD + DH GH = 2 + 4 + 24 GH = 30 32 16 16 2 24 24 G D E F C H B A       4 4 48 8 8

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