Upload File

3.6—bisectors of a triangle warm up 1. draw a triangle and construct the bisector of one angle. 2....

  • Home
  • Documents
  • 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the
13
3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the congruent segments. Draw a picture.

Upload: karin-thornton

Post on 18-Jan-2016

229 views

Category:

Documents


0 download

Report

Tags:

TRANSCRIPT

Page 1: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

3.6—Bisectors of a Triangle

Warm Up

1. Draw a triangle and construct the bisector of one angle.

2. JK is perpendicular to ML at its midpoint K. List the congruent segments. Draw a picture.

Page 2: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

3.6—Bisectors of a Triangle

Objective: Use properties of _____________ bisectors and ___________ bisectors of a __________.

perpendicularangle triangle

Concurrent lines: three or more lines that intersect in the _______ ________

Point of concurrency: the _________ of ________________ of concurrent lines

same point

pointintersection

Page 3: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

The circumcenter can be: inside the triangle (acute triangles), on the triangle (right triangles), or outside the triangle (obtuse triangles). 

_______________ Bisector of a triangle: a ________ that is perpendicular to a side of the triangle at the __________ of the side.

________________ of a triangle: the point of ____________________ of the perpendicular _______________ of a triangle.

Perpendicularline

midpoint

Circumcenterconcurrency

bisectors

Page 4: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the
Page 5: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

Examples: 1. The perpendicular bisectors of ΔHIJ 2. R is the circumcenter of ΔOPQ, meet at K, IJ = 18, and KJ = 12. OS = 10, QR = 12, and PQ = 22.

a. Find HK. a. Find OP.

b. Find IM. b. Find RP.

c. Find KM. c. Find RT.

Page 6: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

________ _____________ of a triangle: a bisector of an _________ of a triangle

_______________ of a triangle:the point of __________________ of the angle bisectors

Angle Bisector angle

Incenterconcurrency

The incenter is always inside the triangle.

Page 7: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the
Page 8: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

Examples: 3. D is the incenter of ΔABC, 4. The angle bisectors of ΔABC meet at P,

a. Find DE. PR = 3 and PC = 5.

b. Find GC. a. Find QP.

b. Find QC.

Page 9: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

Construction – Perpendicular to a line from a point not on the line.

Page 10: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

Construct a perpendicular to the given line and through the given point.

. A.

Page 11: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

B. . 

 

 

Page 12: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

Construct the Circumcenter and the Circumscribed Circle for the triangle.

Page 13: 3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the

Construct the Incenter and the Inscribed Circle for the triangle.


Oak Park Unified School District / Overview · 2014. 6. 11. · Perpendicular Bisectors and Angle Bisectors A perpendicular bisector of a side of a triangle is a line, segment, or

Bisectors, Medians, Altitudes · 2013. 12. 3. · Bisectors, Medians, Altitudes Chapter 5 Section 1 Learning Goal: Understand and Draw the concurrent points of a Triangle The greatest

Chapter 2 : Circumcenter, Orthocenter, incenter, and centroid of triangles Outline Perpendicular bisector, circumcentre and orthocenter Bisectors of angles

5.1 and 5.4 Perpendicular and Angle Bisectors ... 5.1 and 5.4 Perpendicular and Angle Bisectors & ∆ Midsegment Theorem THEOREMS: 1) If a point lies on the perpendicular bisector

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

5.2 Bisectors of a Triangle Geometry Mr. Davenport Fall 2009

Reteaching - niagara.k12.wi.us...Reteaching Bisectors in Triangles The Circumcenter of a Triangle If you construct the perpendicular bisectors of all three sides of a triangle, the

Chapter 5 5-2 Bisectors of angles. Objectives Prove and apply properties of perpendicular bisectors of a triangle. Prove and apply properties of angle

5.1 Bisector and Medians · Bisectors. Medians. and Altitudes Notes — Part A Perpendicular Bisector: a line, segment, or ray that passes through the of a side of and is perpendicular

5.1 Bisectors of Triangles supplemental lesson€¦ · 5.1 Bisectors of Triangles supplemental lesson. GHLesson 52_notes.notebook October 30, 2015 The median of a triangle is a segment

6–3 Angle Bisectors of Trianglesisdmath.weebly.com/uploads/3/8/6/8/38684729/6-3_e... · 2020-03-11 · perpendicular bisectors, every triangle has three angle bisectors. An angle

tiluslm.weebly.comtiluslm.weebly.com/uploads/8/8/0/5/88050222/unit_5-_… · Web view2. How are perpendicular bisectors and angle bisectors of a triangle different? Use the information

A perpendicular bisector is a line found in a triangle

5.1 - 5.2 Bisectors of Triangles and Medians of Triangles ... · 5.1 5.2 Bisectors of Triangles and Medians of Triangles.notebook 13 November 11, 2013 Angle Bisector Theorem If a

9/11/2015 5-1: Special Segments in Triangles Perpendicular Bisectors of a Triangle Defn: Perpendicular Bisector of a Triangle: A segment is a perpendicular

Warm Up 1. Draw a triangle and construct the bisector of one angle

Complexhyperboliclatticesand modulispacesofflatsurfacesip13935/thesis.pdf · 2020. 7. 13. · polyhedron (i.e. maximal dimension facet) is contained in a bisector. Bisectors are

5 Hyperbolic Triangle Geometry - UNC Charlottemath2.uncc.edu/~frothe/3181alllhyp1_5.pdf5 Hyperbolic Triangle Geometry ... A perpendicular bisector or an angle bisector which is a diameter

5.2 Bisectors of Triangles5.2 Bisectors of Triangles Use the properties of perpendicular bisectors of a triangle Use the properties of angle bisectors

Day 36 Triangle Segments and Centers. Today’s Agenda Triangle Segments Perpendicular Bisector Angle Bisector Median Altitude Triangle Centers Circumcenter

Prove and apply properties of perpendicular bisectors of a triangle

chs.rsd407.orgchs.rsd407.org/departments/math/mclaughlin/Geometry....2 - Triangle Bisectors Il 1) Test and Progress Reports 2) Check and Correct Assignment 3) Reminder of Angle Bisector

Bisectors in TrianglesBisectors in Triangles...Holt McDougal Geometry 5-2 Bisectors in Triangles The perpendicular bisector of a side of a triangle does not always pass through the

5.2 Bisectors of a Triangle Geometry Ms. Reser. Objectives Use properties of perpendicular bisectors of a triangle as applied in Example 1. Use properties

Geometry - School of Mathematicskisilv/courses/math255.pdf1.2 Ceva’s theorem ... Theorem 1.3.2 Each angle bisector of a triangle ... Theorem 1.4.3 The external bisectors of any two

5.2 bisectors of a triangle

5.3Use Angle Bisectors of Triangles Theorem 5.5: Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two

- Triangle Problems 1. Using Ceva's Theorem, prove that F) The angle bisectors of any triangle are concurrent. (b) The altitudes of …

5.3 Medians and Altitudes of a Triangle. P. Spitz – Taos H.S. 2 Objectives: Identify properties of perpendicular bisectors and angle bisector Use properties

Holt Geometry 5-2 Bisectors of Triangles Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint

Conic Construction of a Triangle from the Feet of Its Angle Bisectors

5.3 Using Angle Bisectors of Triangles. Vocabulary/Theorems Angle bisector: ray that divides angle into 2 congruent angles Point of concurrency: point

Angle Bisectors and Centroid.gwb - 1/13 - Fri Oct 21 2016 10:33:47 · 2016. 10. 21. · Distance and Angle Bisectors s 5-1-3 5-1-4 CONCLUSION BC THEOREM Angle Bisector Theorem If

Journal Chapter 5 Kirsten Erichsen Perpendicular Bisector and Theorem Angle Bisector and Theorem Concurrency Concurrency of Perpendicular Bisectors Circumcenter

5.1 Notes Bisectors of Triangles. Perpendicular Bisectors We learned earlier that a segment bisector is any line, segment, or plane that intersects a