1 / 28

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.

dylan-copeland
Download Presentation

Honors Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related