1.5 Segment and Angle Bisectors

Slides:

Advertisements

Similar presentations

Sec 1-3 Concept: Use Midpoint and Distance Formulas

Advertisements

Do Now: Solve for x. Calculate the measure of all three angles, and identify each angle as acute, obtuse, or right.

1.5 Segment and Angle Bisectors Goal 1: Bisect a segment Goal 2: Bisect an angle CAS 16, 17.

Objective: Determine if triangles in a coordinate plane are similar. What do we know about similar figures? (1)Angles are congruent (2)Sides are proportional.

Do now: Geo-Activity on page 53

1.5 Segment & Angle Bisectors Geometry Fall 2005 Mrs. Spitz.

Section 1.5 Segment & Angle Bisectors 1/12. A Segment Bisector A B M k A segment bisector is a segment, ray, line or plane that intersects a segment at.

1.5 Segment & Angle Bisectors Geometry Mrs. Blanco.

1.5 Segment Bisectors & Midpoint

Title of Lesson: Segment and Angle Bisectors

Distance and Midpoints

Use Midpoint and Distance Formulas

Chapter 1.3 Notes: Use Midpoint and Distance Formulas Goal: You will find lengths of segments in the coordinate plane.

2.1 Segment Bisectors. Definitions Midpoint – the point on the segment that divides it into two congruent segments ABM.

Goal 1. To be able to use bisectors to find angle measures and segment lengths.

 Find segment lengths using midpoints and segment bisectors  Use midpoint formula  Use distance formula.

1.3 Use Midpoint and Distance Formulas The MIDPOINT of a segment is the point that divides the segment into two congruent segments. A SEGMENT BISECTOR.

Segment and Angle Bisectors. 1.5 Segment and Angle Bisectors GOAL 1 Bisect a segmentGOAL 2 Bisect an Angle.

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.

Lesson 1.3 Midpoint and distance. midpoint The midpoint of a segment is the point that divides the segment into two congruent segments.

1.5 Notes Segment and Angle Bisectors.  The point that divides (or bisects) a segment into two congruent segments.  A segment, ray, line, or plane that.

1.5 Segment & Angle Bisectors p.34. Always Remember! If they are congruent, then set their measures equal to each other!

Midpoint Section 1.5a. Warm Up 1. Graph A (–2, 3) and B (1, 0). 2. Find CD. 3. Find the coordinate of the midpoint of CD. 4. Simplify.

1.5 Angle Bisectors. Angle Bisector A ray that divides an angle into 2 congruent adjacent angles. BD is an angle bisector of

Use midpoint and distance formulas. Vocabulary Midpoint: the midpoint of a segment is the point that divides the segment into two congruent segments (It.

9/14/15 CC Geometry UNIT: Tools of Geometry

1 Lesson 1-3 Use Midpoint and Distance Formula. Warm Up 2 1.Find a point between A(-3,5) and B(7,5). 2.Find the average of -11 and 5. 3.Solve 4.Find 

GEOMETRY Section 1.3 Midpoint.

1-3 Use Midpoint and Distance Formulas Hubarth Geometry.

1.5 Segment & Angle Bisectors

Segments, Rays, and Distance

Midpoint and Distance Formulas

Midpoint and Distance Formulas

Lesson 3 Segment measure and segment bisector

2.1 Segment Bisectors Goal:

Do now Write your comparison on the Do Now Sheet..

Midpoint and Distance in the Coordinate Plane

Bisector A bisector divides a segment into two congruent segments. l

1.3 Midpoint and Distance.

Chapter 1: Essentials of Geometry

1.5 Segment & Angle Bisectors

Chapter 1 Basics of Geometry.

Chapter 1 Basics of Geometry.

1.5 Segment & Angle Bisectors

Segments and Angle Bisectors

Warm-up Name the intersection of plane AEH and plane GHE.

Congruent segments MIDPOINT OF A SEGMENT

1.6: Midpoint and Distance in the Coordinate Plane

1-6 Midpoint and Distance in the Coordinate Plane Warm Up

Use Midpoint and Distance Formulas

1.3 Use Midpoint and Distance Formulas

Use Midpoint and Distance Formulas

Angles and Bisectors.

1.6: Midpoint and Distance in the Coordinate Plane

The Distance and Midpoint Formulas

1.3 Segments, Rays, and Distance

1.5 Segment & Angle Bisectors

1.3 Segments, Midpoints and distance formula

Chapter 1 Section 3 Midpoint and Distance

Def: Congruent Line Segments:

Warm Up Construct a segment AB.

Find each segment length and determine if AB is congruent to CD

Coordinate Distance Congruent Midpoint Bisector Angle Sides Vertex

Find the Other Endpoint of a Segment

1.5 Segment and Angle Bisectors

Segment and Angle Bisectors

Segment and Angle Bisectors

1-6 Midpoint and Distance in the Coordinate Plane Warm Up

1.3 Use Midpoint and Distance Formulas

1.3 Use Midpoint and Distance Formulas

Presentation transcript:

1.5 Segment and Angle Bisectors Geometry 1.5 Segment and Angle Bisectors

Bisecting a Segment The midpoint of a segment is the point that divides, or bisects (divide into two equal parts), the segment into two congruent segments. A segment bisector is a segment, ray, line, or plane that intersects a segment or its midpoint

Finding the Midpoint If you know the coordinates of the endpoints of a segment, you can calculate the coordinates of the midpoint. You simply take the mean, or average, of the x-coordinates and of the y-coordinates. This method is summarized as the Midpoint Formula

Midpoint Formula

Find the Midpoint Graph the points A(-2, 3) and B(5, -2) Use the Midpoint Formula to find the coordinates of the midpoint of segment AB.

Find the Midpoint Graph the points D(3, 5) and E(-4, 0) Use the Midpoint Formula to find the coordinates of the midpoint of segment DE.

Find the Other Endpoint of a Segment Graph the points X(-3, 1) and M(3, -4) The midpoint of segment XY is M. One endpoint is X. Find the coordinates of the other endpoint.

Find the Other Endpoint of a Segment Graph the points R(-1, 7) and M(2, 4) The midpoint of segment RP is M. One endpoint is R. Find the coordinates of the other endpoint.

Bisecting an Angle An angle bisector is a ray that divides an angle into two adjacent angles that are congruent.

The ray FH bisects the angle EFG The ray FH bisects the angle EFG. Given that the measure of angle EFG = 120 degrees, what are the measures of angle EFH and angle HFG? Example 1

Example 2 Angle CBA is bisected by ray BD. The measure of angle DBA is 65 degrees. Find the measure of angle CBA.

Example 3 In the diagram, ray RQ bisects angle PRS. The measures of the two congruent angles are (x+40) degrees and (3x – 20) degrees. Solve for x. (x + 40) (3x – 20)