STARTER! Find the length of SU if: S = ( -11, 15) and U = (-5, 23)

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Presentation transcript:

STARTER! Find the length of SU if: S = ( -11, 15) and U = (-5, 23)

Geometry Chapter 1 section 5 Congruence and Midpoints

Equal in measure M G B A We Say GM

Why Not Equal? Congruent means equal in measure But not equal in position or orientation

What can be Congruent? Can Lines be congruent? Can Rays be congruent? Can Points be congruent? Can Planes be congruent? Can Line Segments be congruent?

Midpoint of a segment If point M is the midpoint of DE then M is between D and E ME

What kind of figures have midpoints Can Lines have midpoints? Can Rays have midpoints? Can Points have midpoints? Can Planes have midpoints? Can Line Segments have midpoints?

If M is the midpoint of FS If FS = 10 Find FM

If M is the midpoint of PQ PQ = 3x + 14 PM = 2x – 3 Find QM

Midpoint Formula To find the midpoint of points ( x 1, y 1 ) and (x 2, y 2 ) x 1 + x 2 y 1 + y (),

Find the midpoint JG J = ( 3, 10) G = ( -5, 2)

Find the midpoint NV N = ( 8, -11) V = ( 6, -3)

Find an endpoint given an endpoint and the midpoint D is the midpoint of KJ D = (5, 3)J = ( 12, - 4) Find the coordinates of K

Find an endpoint given an endpoint and the midpoint B is the midpoint of HG H = (8, 9)B = ( -2, -4) Find the coordinates of G

A figure that goes through the midpoint of a segment is said to bisect the segment A GR Bisects AB if D is the midpoint of AB B R G D

Do Now! Page 41 Problems 7 – 10 Problems 16 – 38 even Problems