Bellringer

1.4 Measuring Segments and Angles

Postulate 1-5 Ruler Postulate

Two segments with the same length

Comparing Segments lengths BA C DE

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

Using the Segment Addition Postulate If DT = 60, find the value of x. Then find DS and ST. DS T 2x - 83x - 12 DS + ST = DT (2x – 8) + (3x – 12) = 60 5x – 20 = 60 5x = 80 x = 16 Segment Addition Postulate Substitution Simplify Add 20 to each side Divide each side by 5 DS + ST = DT Substitute x = 16 DS = 2x – 8 = 2(16) – 8 = 24 ST = 3x – 12 = 3(16) – 12 = 36

Using the Segment Postulate If DT = 100. Find the value of x. Then find DS and ST. x = 15 DS = 40 ST = 60 DS T 4x - 202x + 30

Midpoint

Finding Lengths A CB 2x + 13x - 4 AC = CB 2x +1 = 3x - 4 2x + 5 = 3x 5 = x Definition of Midpoint Substitution Add 4 to each sides Subtract 2x from each side AC = 2x + 1 = 2(5) + 1 = 11 CB = 3x – 4 = 3(5) – 4 =11 AC + CB = AB = 22

Finding Lengths X ZY 30

Homework Pg. 29 #’s 1 – 4, 8-15

Bellringer If XT = 12 and XZ = 21, then TZ = 9 X TZ

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

Congruent Angles

Homework Pg. 30 #’s all