1 1c midpoint segment congruence and segment addition
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1.1c: 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.

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1.1c: Midpoint ,Segment Congruence, and Segment Addition

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1 1c midpoint segment congruence and segment addition

1.1c: 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.

M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope

GSE


Midpoint

Midpoint

  • The point that bisects a segment.

  • Bisects?

    splits into 2 equal pieces

12x+3 10x+5

A M B

12x+3=10x+5

2x=2

x=1


Segment bisector

Segment Bisector

  • A segment, ray, line, or plane that intersects a segment at its midpoint.

k

A

M

B


Midpoint formula

Midpoint Formula

  • Used for finding the coordinates of the midpoint of a segment in a coordinate plane.

  • If the endpoints are (x1,y1) & (x2,y2), then


Ex find the midpoint of jt if j 3 5 t 4 2

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

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

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

B

B


1 1c midpoint segment congruence and segment addition

Ex: The midpoint of AB is M(-3,5).

One endpoint is A(4,6). Find the coordinates of B.


1 1c midpoint segment congruence and segment addition

  • 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.

  • 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

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.

C

B

A


Seg add post example

Seg. Add. Post. Example

  • If J is between H and K and HJ=5x-3 , JK = 4x, HK = 8x, find HJ, JK, HK

  • Ans: Draw a diagram


Example

Example

  • M is between L and N. Find each measurement if: LM = 4x+6 ,

    LN = 5x+10

    MN = 3x – 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

Ex: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG.

D

E

F

G

FG=2

DF=7

DG=9

EG=7


Assignment

Assignment


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