1 1 c Midpoint Segment Congruence and Segment

1. 1 c: Midpoint , Segment Congruence, and Segment Addition CCSS G-CO. 1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. GSE M(G&M)– 10– 9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope

Midpoint • The point that bisects a segment. • Bisects? splits into 2 equal pieces 12 x+3 A 12 x+3=10 x+5 2 x=2 x=1 10 x+5 M B

Segment Bisector • A segment, ray, line, or plane that intersects a segment at its midpoint. k A M B

Midpoint Formula • Used for finding the coordinates of the midpoint of a segment in a coordinate plane. • If the endpoints are (x 1, y 1) & (x 2, y 2), then

Ex: Find the midpoint of JT if J(-3, 5) & T(4, 2). x’s y’s

Ex. Find the midpoint of DC and label it point A A

Ex: The midpoint of AB is M(2, 4). One endpoint is A(-1, 7). Find the coordinates of B. B B

Ex: The midpoint of AB is M(-3, 5). One endpoint is A(4, 6). Find the coordinates of B.

A major league baseball diamond is a square having side lengths 90 feet. Overlay a rectangular coordinate system on the baseball diamond so that: -the origin is at home plate -the positive x-axis is along the first base line -the positive y-axis is along the third base line. i. What are the coordinates of first, second, and third base? ii. What is the distance from home plate to second base? iii. If the right fielder is at (305, 10), how far is the right fielder from second base? iv. Suppose you want to position the pitching mound at equal distances from second base and home plate. What coordinates would the pitching mound have? v. The left fielder was at (15, 250) and threw a ball into the infield that was cut off by the shortstop at (8, 120). The shortstop was in the middle between the left fielder and pitcher. What are the coordinates of the pitcher?

Post. 2: Segment Addition Postulate. • If B is between A & C, then AB + BC = AC. • If AB + BC = AC, then B is between A & C. A B C

Seg. Add. Post. Example • If J is between H and K and HJ=5 x-3 , JK = 4 x, HK = 8 x, find HJ, JK, HK • Ans: Draw a diagram

Example • M is between L and N. Find each measurement if: LM = 4 x+6 , LN = 5 x+10 MN = 3 x – 4 LM + MN = LN LM =4(4)+6 = 22 MN = 3(4)-4 = 8 LN = 5(4)+10 = 30

Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG. D E F FG=2 DF=7 DG=9 EG=7 G

Assignment