Bell Work 8/26-8/27

Outcomes• I will be able to:• 1) Define and Use new vocabulary: midpoint,

bisector, segment bisector, construction, Midpoint Formula and angle bisector.

• 2) Bisect a segment/angle by measuring, by folding, and by algebraic reasoning.

• 3) Use the Midpoint Formula to calculate segment midpoints on a coordinate plane.

Agenda• BellWork• Outcomes • Agenda• Announcements – Quiz review will be

Weds/Thurs/Friday - Honors Application• Paper Folding Investigation• 1.5 Daily Notes and PPt• IP - Worksheet

Folding Bisectors ActivityEvery Person needs:• Black/dark sharpie or felt tip marker• 2 sheets of paper

Every Table Needs:• Ruler• Protractor• Textbook open to page 33

• Follow instructions and then write answers to the two questions under your BellWork in your notebook.

1.5 Segment and Angle Bisectors

Some Definitions:• Midpoint of a Segment – is the point that

divides, or bisects, the segment into two congruent segments.

– M is the midpoint of AB if M is on AB – and AM = MB

MA B

• Segment Bisector – is a segment, ray, line, or plane that intersects a segment at its midpoint.

• CD is a bisector of AB.

A M B

D

C

Midpoint Formula• If A(x1, y1) and B(x2, y2) are points in a coordinate

plane, then the midpoint of AB has coordinates

M

2,

22121 yyxx

A(x1, y1)

B(x2, y2)

Midpoint Formula

• When given two endpoints, simply plug into the midpoint formula after labeling the points.

• Midpoint =

• We Do - Find the midpoint of points: D(3,5) and E(-4,0)

• You Do - Find the midpoint of the segment AB: with A(-2,6) and B(3,10)

2,

22121 yyxx

Midpoint Formula

We Do -• The midpoint of segment XY is M(3,-4). One

endpoint is Y(-3,-1). Find the coordinates of point X. Draw a diagram…

Midpoint Formula

You Do-• The midpoint of segment JK is M(0,0.5). One

endpoint is J(2,-2). Find the coordinates of point K. Draw a diagram…

Angle Bisector

• An Angle Bisector - is a ray that divides an angle into two adjacent angles that are congruent. Ray CD bisects ∠ACB.

• ∠ACD and ∠BCD are congruent.

DCBACD

Example 1

Example 2

Example 3 workspace

Exit Ticket1)Use complete sentences for the following:What is a midpoint?What is a segment Bisector?2) Find the coordinates of the midpoint of AB, where A(5,4) and B(-3,2)3)Solve for x.