5.1 Perpendiculars and Bisectors. Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from.

Slides:

Advertisements

Similar presentations

GEOMETRY HELP Use the map of Washington, D.C. Describe the set of points that are equidistant from the Lincoln Memorial and the Capitol. The Converse of.

Advertisements

Bisectors in Triangles Academic Geometry. Perpendicular Bisectors and Angle Bisectors In the diagram below CD is the perpendicular bisector of AB. CD.

Chapter 5 Properties of Triangles Perpendicular and Angle Bisectors Sec 5.1 Goal: To use properties of perpendicular bisectors and angle bisectors.

Geo: Sec 5.1 Perpendiculars & Bisectors Thm 5.1 Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant.

5.1 Perpendiculars and Bisectors Geometry Mrs. Spitz Fall 2004.

5.1 Perpendiculars and Bisectors

4-7 Median, Altitude, and Perpendicular bisectors.

5.1 Perpendiculars and Bisectors Geometry Mrs. Spitz Fall 2004.

5.1: Perpendicular Bisectors

Using properties of Midsegments Suppose you are given only the three midpoints of the sides of a triangle. Is it possible to draw the original triangle?

Chapter 5 Congruent Triangles. 5.1 Perpendiculars and Bisectors Perpendicular Bisector: segment, line, or ray that is perpendicular and cuts a figure.

Section 5.2 Use Perpendicular Bisectors. Vocabulary Perpendicular Bisector: A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

5.1 Perpendicular and Angle Bisectors

5.2 Use Perpendicular Bisectors

Keystone Geometry. » There are four types of segments in a triangle that create different relationships among the angles, segments, and vertices. ˃Medians.

5-2 Perpendicular and Angle Bisectors Learning Goals 1. To use properties of perpendicular bisectors and angle bisectors.

Chapter 5 Angle Bisectors. Angle Bisector A ray that bisects an angle into two congruent angles.

5.2 Perpendicular and Angle Bisectors

5-2 Perpendicular and Angle Bisectors. A point is equidistant from two objects if it is the same distance from the objects.

Warmup P.254 # Bisectors in Triangles Learning Target I can use properties of perpendicular bisectors and angle bisectors to solve problems.

4.5 Isosceles and Equilateral Triangles. Isosceles Triangles At least two sides are of equal length. It also has two congruent angles. Base Angles Base.

Find the missing angle ?0?0. Special Segments in Triangles.

Chapter 5.1 Common Core - G.CO.10 Prove theorems about triangles…the segment joining the midpoint of two sides of a triangle is parallel to the third side.

5.1 Perpendiculars and Bisectors Geometry Mrs. Spitz Fall 2004.

Warm Up Week 7 Label the information: AB C D 1) ∠C is a right angle. 2) ∠A ≅ ∠B 3) AB = 8 4) bisects.

Section 5-2 Bisectors in Triangles. Vocabulary Distance from a point to a line: the length of the perpendicular segment from the point to the line.

CHAPTER 5 Relationships within Triangles By Zachary Chin and Hyunsoo Kim.

5.1 midsegments of triangles Geometry Mrs. Spitz Fall 2004.

Chapter 5 More Triangles. Mr. Thompson More Triangles. Mr. Thompson.

Perpendicular Bisectors ADB C CD is a perpendicular bisector of AB Theorem 5-2: Perpendicular Bisector Theorem: If a point is on a perpendicular bisector.

Lesson 5-1: Perpendicular & Angle Bisectors Rigor: apply the perpendicular bisector theorem, the angle bisector theorem, and their converses Relevance:

Section 5-1 Perpendiculars and Bisectors. Perpendicular bisector A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

Bisectors in Triangles Section 5-2. Perpendicular Bisector A perpendicular tells us two things – It creates a 90 angle with the segment it intersects.

Chapter 5.3 Notes: Use Angle Bisectors of Triangles Goal: You will use angle bisectors to find distance relationships.

Chapter 5.2 Bisectors in Triangles Reminder: Bring your textbook for cd version!

 In Chapter 1, you learned the definition of a midpoint of a segment. What do you think a midsegment of a triangle is?  Find the midpoint of AB: o A(-2,

Section 5.2 Use Perpendicular Bisectors. Vocabulary Perpendicular Bisector: A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

Concurrencies for Medians, Altitudes, and Bisectors

5.6 Angle Bisectors and Perpendicular Bisectors

Daily Warm-Up Quiz F H, J, and K are midpoints 1. HJ = __ 60 H 65 J FG = __ JK = __ m < HEK = _ E G Reason: _ K 3. Name all 100 parallel segments.

Isosceles Triangles Theorems Theorem 8.12 – If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

Perpendicular and Angle Bisectors Perpendicular Bisector – A line, segment, or ray that passes through the midpoint of a side of a triangle and is perpendicular.

5.2: Bisectors in Triangles Objectives: To use properties of perpendicular and angle bisectors.

5.1 Perpendiculars and Bisectors Geometry Mrs. Spitz Fall 2004.

5.3.1 Use Angle Bisectors of Triangles Chapter 5: Relationships within Triangles SWBAT: Define and use Angle Bisector Theorem. Define incenter You will.

5-2 Perpendicular and Angle Bisectors. Perpendicular Bisectors A point is equidistant from two objects if it is the same distance from each. A perpendicular.

Warm Up Week 7 1) What is the value of x? 28 ⁰ x⁰x⁰ 3x ⁰.

Chapter 5: Properties of Triangles Section 5.1: Perpendiculars and Bisectors.

Section 5.2 Perpendicular Bisectors Chapter 5 PropertiesofTriangles.

Objectives Prove and apply theorems about perpendicular bisectors.

Isosceles Triangles.

LESSON 5-2 BISECTORS IN TRIANGLES OBJECTIVE:

5.1 Perpendiculars and Bisectors

Table of Contents Date: Topic: Description: Page:.

Perpendicular Bisectors

Midsegments of Triangles

4.1 warm-up A triangle is enlarged by a scale factor of 9. If the length of one side of the larger triangle is centimeters, what is the length.

Bisectors, Medians and Altitudes

5.1 Perpendiculars and Bisectors

5.2 Bisectors in Triangles

Triangle Segments.

6.1 Perpendicular and Angle Bisectors

6.1 Perpendicular and Angle Bisectors

5.2 Bisectors in Triangles

Module 15: Lesson 5 Angle Bisectors of Triangles

SPECIAL SEGMENTS.

To Start: 20 Points 1. What is a midsegment?

5-1 Bisectors of Triangles

Chapter 5 Congruent Triangles.

Objective: To use properties of perpendicular and angle bisectors.

Presentation transcript:

5.1 Perpendiculars and Bisectors

Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. If CP is the perpendicular bisector of AB, then CA = CB. A P B C

Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. If CA=CB, then C lies on the perpendicular bisector of

In the diagram shown, MN is the perpendicular bisector of ST. What segment lengths in the diagram are equal? Explain why Q is on MN T M N S Q 12

Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. If m<BAD = m<CAD, then DB = DC. A B C D

Converse of the Angle Bisector Theorem If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. If DB=DC, then m<BAD = m<CAD

Use the diagram to answer the following. In the diagram, F is on the bisector of < DAE. If m<BAF = 50, then m<CAF = ____ If FC = 10, then FB = ____ Is triangle ABF congruent to triangle ACF? Explain. A B D G F C E

Closing Question: