Applied Geometry Lesson 2 3 Congruent Segments Objective

Applied Geometry Lesson 2 – 3 Congruent Segments Objective: Learn to identify congruent segments and find the midpoints of segments.

Congruent Segments: segments that have the same length. Definition of Congruent segments Segments are equal AB = CD Measure of the segments are equal

Use the number line to determine whether the statement is true or false. Explain. 1. is congruent to 2. T 7=7 3. T 4=4 4.

Theorems A statement that can be justified by logical reasoning. It must be proven true before it is accepted as true.

Theorem 2 -1 l Congruence of segments is reflexive

Theorem 2 -2 l Congruence of segments is symmetric.

Theorem 2 -3 l Congruence of segments is transitive.

Example True or False. Explain your reasoning. Segment JK is congruent to segment KJ True, by reflexive and substitution. True, transitive seg. CD same as seg. DC

Midpoint A point M is the midpoint of a segment ST if and only if M is between S and T and SM = MT.

Example In the figure, C is the midpoint of Find the value of x. AC = CB since C is the midpoint. 5 x – 6 = 2 x 3 x = 6 x=2 check: 5 x – 6 = 2 x 5(2) – 6 = 2(2) 10 – 6 = 4 4=4

Example W is the midpoint of segment XY. If XW = a + 11 and WY = 2 a – 5, find the value of a. Draw a picture to help. a + 11 = 2 a - 5 11 = a - 5 16 = 2 a 8=a

Bisect To separate a geometric figure into congruent parts using a point, line, ray, segment, or plane.

Homework Pg. 65 1 – 7 all, 8 – 28 E