Unit 1 Foundations of Geometry Segments and Rays

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Presentation transcript:

Unit 1 Foundations of Geometry Segments and Rays Post. 1-2-2: Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. A B C G is between F and H, FG = 6, and FH = 11. Find GH. Draw a diagram representing the situation. F G H 6 11 FH = FG + GH Seg. Add. Postulate 11 = 6 + GH Substitute 6 for FG and 11 for FH.

Unit 1 Foundations of Geometry Segments and Rays Mr. Mack’s happy home The distance from Mr. Mack’s house to the Mellow Mushroom is 12 miles. If Mr. Rick’s house is the midpoint between Mellow Mushroom and Mr. Mack’s house, how far does Mr. Mack live from Mr. Rick? Mr. Rick’s house Mellow Mushroom

Unit 1 Foundations of Geometry Segments and Rays Midpoint: a point that divides a segments into two congruent segments. We say point B bisects segment AC A B C If AB = 25, find the value of AN and NB. M is the midpoint of RT. Find RM, MT, and RT.

Unit 1 Foundations of Geometry Angles Angle: is formed by two rays with the same endpoint. The rays are the sides of the angles. The endpoint is the vertex of the angle. B T Q 1 The sides of the angle are BQ and BT. The vertex is B. The angle can be named: B, TBQ, QBT, and 1. A C B D E Which is angle A?

Unit 1 Foundations of Geometry Angles Special Angles x right angle x = 90 x obtuse angle 90<x<180 x acute angle 0<x<90 x straight angle x = 180

Unit 1 Foundations of Geometry Angles Post. 1-8: 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. A B C O m1+m2 = mAOC A B C O 1 2 1 2 m1+m2 = 180 mDEG = 115°, and F is in interior of DEG. Find mFEG if mDEF = 48°.

Unit 1 Foundations of Geometry Angles An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM. KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

Unit 1 Foundations of Geometry Angles KM bisects JKL, mJKM = (2x + 9)°, and mJKL = (6x – 10)°. Find mLKM.

Unit 1 Foundations of Geometry Angles If mFPB=70° and mFPS=110° find all angle measures. F H P R S B

Unit 1 Foundations of Geometry Angles Special Angle Pairs Adjacent Pair: Linear Pair… Supplementary: Complimentary… Vertical angles… Common vertex, share side, no common interior points, coplanar Adjacent angles that form straight line Two angles whose sum = 180° Two angles whose sum = 90° Two nonadjacent angles formed by intersecting lines.

Unit 1 Foundations of Geometry Angles Name all adjacent angle pairs 1 4 2 3 5 Name all linear angle pairs Name all vertical angle pairs What angle is complementary to 2x -28°? What angle is supplementary to 3x + 88°?

Homework 1.3(24):12-14,17,18,29,31,33,41,43,44,47 1.4(32):15-17,19,20,27,31,33,44,46