5.1 Special Segments in Triangles Learn about Perpendicular Bisector Learn about Medians Learn about Altitude Learn about Angle Bisector.

Slides:

Advertisements

Similar presentations

5-1 Special Segments in Triangles

Advertisements

Day 7.

Unit 2 Find the Midpoint of a Line Segment Learning Goals: I can find the midpoint of a line segment by applying what I know about averages. I can solve.

Section 4.7 Medians, Altitudes, and Perpendicular Bisectors

4-7 Median, Altitude, and Perpendicular bisectors.

Medians, Altitudes and Perpendicular Bisectors

A perpendicular bisector is a line found in a triangle CIRCUMCENTER It cuts the side into two equal parts And because it's perpendicular it makes two.

 Definition:  A line that passes through the midpoint of the side of a triangle and is perpendicular to that side.

Basic Definitions in Geometry

Medians, Altitudes, and Angle Bisectors Honors Geometry Mr. Manker.

Aim: Do Now: Ans: 5 5 miles 4 miles Ans: 3 miles P A B C

Honors Analysis.  Solve linear equations  Write linear equations based on application problems  Write linear equations involving supplements and.

Aim: Isosceles Triangle Course: Applied Geometry Aim: What is an Isosceles Triangle? Do Now: What type of triangle has sides of 3, 6, 8?

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

Objectives To define, draw, and list characteristics of: Midsegments

Drill Write your homework in your planner Take out your homework Solve for x:

Special Segments in Triangles Section 5-1. Perpendicular Bisector - a line or line segment that passes through the midpoint of a side of a triangle and.

Unit 2 Test Review Geometry WED 1/22/2014. Pre-Assessment Answer the question on your own paper.

Lesson 12 – Points of Concurrency II

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.

Vocabulary Unit 4 & 5. Equilateral/Equiangular Triangle A triangle with 3 congruent sides and 3 congruent angles.

Points of Concurrency The point where three or more lines intersect.

Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4.

5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify.

SPECIAL SEGMENTS IN TRIANGLES KEYSTONE GEOMETRY. 2 SPECIAL SEGMENTS OF A TRIANGLE: MEDIAN Definition of a Median: A segment from the vertex of the triangle.

What is an Isosceles Triangle? A triangle with at least two congruent sides.

A triangle in which exactly one angle is obtuse is called an ___________ triangle.

Chapter 5.2 & 5.3 BISECTORS, MEDIANS AND ALTITUDES.

Median, Angle bisector, Perpendicular bisector or Altitude Answer the following questions about the 4 parts of a triangle. The possible answers are listed.

Ch. 5 – Properties of Triangles

5-2 Median & Altitudes of Triangles

How do we analyze the special segments that exist inside triangles? Agenda: Warmup Go over homework Segments inside triangles notes/practice QUIZ Thursday.

MEDIANS AND ALTITUDES OF TRIANGLES (SPECIAL SEGMENTS) Unit 4-4.

Special lines in Triangles and their points of concurrency Perpendicular bisector of a triangle: is perpendicular to and intersects the side of a triangle.

1 Def: Median Def: A median of a triangle is a line segment that joins any vertex of the triangle to the midpoint of the opposite side. Every triangle.

Integrated Math II Lesson 22 Special Segments in Triangles.

4.4 Altitudes, Medians, and Perpendicular Bisectors

Bisectors, Medians, and Altitudes

5-1 Special Segments in Triangles

Medians, Altitudes and Perpendicular Bisectors

Special Segments in a Triangle

12 Chapter Congruence, and Similarity with Constructions

Perpendicular Bisector

You need your journal The next section in your journal is called special segments in triangles You have a short quiz.

Geometry Vocabulary Geometry - branch of mathematics that deals with points, lines, planes and solids and examines their properties. Types of the line.

Date: Topic: Altitudes, Medians, and Bisectors ____ (6.4)

Triangle Fundamentals

Medians and Altitudes of a Triangle

Vocabulary and Examples

Special Segments in Triangles

Bisectors, Medians and Altitudes

Chapter 5 Types of Segments

Lines, Angles and Triangles

Line Segments Associated with Triangles Ch. 5-1

Geometry Lesson 5.4.

Triangle Segments.

Definition of a Median of a Triangle A median of a triangle is a segment whose endpoints are a vertex and a midpoint of the opposite side.

4-7 Medians, Altitudes, and Perpendicular Bisectors

Medians, Altitudes, & Perpendicular Bisectors

Centroid Theorem By Mario rodriguez.

4-7 Medians, Altitudes, and Perpendicular Bisectors

Corresponding Parts of Similar Triangles

MID-TERM STUFF HONORS GEOMETRY.

Lesson: 5.1 Special Segments in Triangles Pages: 238 – 241 Objectives:

12 Chapter Congruence, and Similarity with Constructions

Warm Up - Copy each of the following into your notebook, then solve.

SPECIAL SEGMENTS.

Midpoint and Median P9. The midpoint of the hypotenuse of a right triangle is equidistant from the 3 vertices. P12. The length of a leg of a right triangle.

Presentation transcript:

5.1 Special Segments in Triangles Learn about Perpendicular Bisector Learn about Medians Learn about Altitude Learn about Angle Bisector

Definitions: Perpendicular Bisector A line that passes through the midpoint of a side of a triangle and is perpendicular to same side. Median A line segment that connects a vertex of triangle with its opposite side midpoint

Definitions Altitude A line segment with one end point at a vertex and other perpendicular to its opposite side Angle Bisector: A line segment that divides a given angle into two equal halves

Perpendicular Bisector A line that passes through the midpoint of a side of a triangle and is perpendicular to that side.

Median A line segment that connects a vertex of triangle with its opposite side midpoint

Altitude A line segment with one end point at a vertex and other perpendicular to its opposite side

Angle Bisector A line segment that divides a given angle into two equal halves

Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint

Example: Given Altitude Solve for x: Solution: Altitude: A line segment with one end point at a vertex and other perpendicular to its opposite side 4x + 10 = 90 4x = 80 x = 20 BC = 2x +(3x - 4) BC = = 96

Example: Given Angle Bisector Solve for x: Solution: Angle Bisector: A line segment that divides a given angle into two equal halves 2( x + 6 )= 4x- 6 2x + 12 = 4x - 6 2x = 18 x = 9 ABC = 4x - 6 ABC = 30

Example: Given Angle Bisector Solve for x: Solution: Angle Bisector: A line segment that divides a given angle into two equal halves 6x + 3 = 5x + 9 x + 3 = 9 X = 6

Example: Given Angle Bisector Solve for x: Solution: Angle Bisector: A line segment that divides a given angle into two equal halves 2(3x – 7) = 4x 6x -14 = 4x 2x = 14 X = 7

Example: Given Median Solve for x: Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint 2(5x – 3) = 8x 10x - 6 = 8x 2x = 6 X = 3

Example: Given Median Solve for x: Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint x – 4 = 2x = x - 10 x = 6

Example: Given Median Solve for x: Solution: Median: A line segment that connects a vertex of triangle with its opposite side midpoint x + 3 = 2x = x - 17 x = 20 AB = AB = 13