Bellringer 1 4 Measuring Segments and Angles Postulate
Bellringer •
1. 4 Measuring Segments and Angles
Postulate 1 -5 Ruler Postulate •
• Two segments with the same length
Comparing Segments lengths • A B C D E
Postulate 1 -6 Segment Addition Postulate • If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC
T Using the Segment Addition Postulate • If DT = 60, find the value of x. Then find DS and ST. D • • 2 x - 8 • DS + ST = DT (2 x – 8) + (3 x – 12) = 60 • • 5 x – 20 = 60 • 5 x = 80 • x = 16 Substitute x = 16 DS = 2 x – 8 = 2(16) – 8 = 24 ST = 3 x – 12 = 3(16) – 12 = 36 S 3 x - 12 T Segment Addition Postulate Substitution Simplify Add 20 to each side Divide each side by 5
Using the Segment Postulate • If DT = 100. Find the value of x. Then find DS and ST. D • x = 15 • DS = 40 • ST = 60 4 x - 20 S 2 x + 30 T
Midpoint •
Finding • Lengths • • AC = CB 2 x +1 = 3 x - 4 2 x + 5 = 3 x 5=x A • • • AC = 2 x + 1 = 2(5) + 1 = 11 • CB = 3 x – 4 = 3(5) – 4 =11 • AC + CB = AB 11 + 11 = 22 2 x + 1 C 3 x - 4 B Definition of Midpoint Substitution Add 4 to each sides Subtract 2 x from each side
Finding Lengths • 30 X Z Y
Homework • Pg. 29 #’s 1 – 4, 8 -15
Bellringer X T Z • If XT = 12 and XZ = 21, then TZ = 9
1. 4 CONTINUED Measuring Segments and Angles
• Is formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle.
Naming Angles •
Classifying Angles •
Postulate 1 -8 Angle Addition Postulate •
Using the Angle Addition Postulate •
Using the Angle Addition Postulate •
Congruent Angles •
Homework • Pg. 30 #’s 16 -28 all
- Slides: 22