Geometry 1.2: Segments and Congruence SWLT: Use segment postulates to identify congruent segments.

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Presentation transcript:

Geometry 1.2: Segments and Congruence SWLT: Use segment postulates to identify congruent segments

Ruler Postulate The points on a line can be matched one to one with real numbers. The real number that corresponds to a point is the coordinate of the point The distance between points A and B, written as AB, is the absolute value of the difference of coordinates of A and B ABAB x1x2x1x2 AB = |x 2 – x 1 |

Segment Addition Postulate If B is between A and C, then AB + BC = AC (Converse): If AB + BC = AC, then B is between A and C. AB C AC

Application of Segment Addition Postulate: Use the Diagram to find KL 38 J15KL JL = JK + KL 38 = 15 + KL 23 = KL Segment Addition Postulate Substitute 38 and 15 Simple Algebra will give you a solution 23

Comparing Segments for Congruence Plot the below points in a coordinate plane. Then determine whether FG and HJ are congruent F(4, 5), G(-1, 5) H(3, 3), J(3, -2) Horizontal segment: Subtract x-coordinates of the endpoints FG = |4 – (-1)| = 5 Vertical Segment: Subtract the y-coordinates of the endpoints HJ = |3 – (-2)| = 5 FG and HJ have the same length. Therefore FG ≅ HJ

On your Own Find QS and PQ 55 PQ 31R 30S Given: A (-2, -1), B (4, -1), C(3, 0), and D (3, 5). Are AB and CD Congruent?