5.3 Concurrent Lines, Medians, and Altitudes

Slides:

Advertisements

Similar presentations

5.1 Bisector, Medians, and Altitudes

Advertisements

Lesson 5-1 Bisectors, Medians, and Altitudes. Ohio Content Standards:

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

5-3 Concurrent Lines, Medians, Altitudes

NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3. Any point that is on the perpendicular bisector of a segment is equidistant from the endpoints of the.

Concurrent Lines Geometry Mrs. King Unit 4, Day 7.

Medians, Altitudes and Concurrent Lines Section 5-3.

Properties of Triangles

5.3 - Concurrent Lines, Medians, and Altitudes

Thinking Page… Directions: Take out your math encyclopedia and review your notes for this unit. Write two paragraphs using complete sentences and correct.

1 Triangle Angle Sum Theorem The sum of the measures of the angles of a triangle is 180°. m ∠A + m ∠B + m ∠C = 180 A B C Ex: If m ∠A = 30 and m∠B = 70;

 Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side  Theorem 5.1  Any point.

Day 4 agenda Go over homework- 5 min Warm-up- 10 min 5.3 notes- 55 min Start homework- 20 min The students will practice what they learned in the computer.

Chapter 5.3 Concurrent Lines, Medians, and Altitudes

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

By: Isaac Fernando and Kevin Chung.  Do Now: what is a point of concurrency?

Geometry Grab your clicker and get ready for the warm-up.

Median and Altitude of a Triangle Sec 5.3

Section 5-3 Concurrent Lines, Medians, Altitudes SPI 32J: identify the appropriate segment of a triangle given a diagram and vs (median, altitude, angle.

Points of Concurrency Triangles.

Special Segments of Triangles

5.4 Medians and Altitudes A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side. –A triangle’s three medians.

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.

Geometry B POINTS OF CONCURRENCY. The intersection of the perpendicular bisectors. CIRCUMCENTER.

Chapter 10 Section 3 Concurrent Lines. If the lines are Concurrent then they all intersect at the same point. The point of intersection is called the.

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.

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.

SPECIAL SEGMENTS OF TRIANGLES SECTIONS 5.2, 5.3, 5.4.

5.3 Concurrent Lines, Medians, and Altitudes Stand 0_ Can you figure out the puzzle below??? No one understands!

Homework Quiz. Warmup Need Graph Paper/Compass 5.3 Concurrent Lines, Medians, and Altitudes.

LESSON FIFTEEN: TRIANGLES IN TRAINING. MORE TRIANGLE PROPERTIES In the last lesson, we discussed perpendicular bisectors and how they intersect to create.

5-2 Median & Altitudes of Triangles

Chapter 5, Section 1 Perpendiculars & Bisectors. Perpendicular Bisector A segment, ray, line or plane which is perpendicular to a segment at it’s midpoint.

Medians, and Altitudes. When three or more lines intersect in one point, they are concurrent. The point at which they intersect is the point of concurrency.

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

Chapter 5: Relationships within Triangles 5.3 Concurrent Lines, Medians, and Altitudes.

Bisectors, Medians, and Altitudes

Section 5 – 3 Concurrent Lines, Medians, and Altitudes

Chapter 5 Lesson 3 Objective: To identify properties of medians and altitudes of a triangle.

Medians, Altitudes and Perpendicular Bisectors

Relationships in Triangles

Lesson 14.3 The Concurrence Theorems

Special Segments in a Triangle

Triangle Centers Points of Concurrency

Transformations Transformation is an operation that maps the original geometric figure, the pre-image , onto a new figure called the image. A transformation.

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

Medians and Altitudes of a Triangle

Vocabulary and Examples

Special Segments in Triangles

Lines, Angles and Triangles

Bisectors, Medians and Altitudes

Concurrent Lines, Medians, Altitudes

Triangle Segments.

5-1 HW ANSWERS Pg. 327 # Even 18. CF 10. PS = DA & DB

4-7 Medians, Altitudes, and Perpendicular Bisectors

Centroid Theorem By Mario rodriguez.

Medians and Altitudes Median – A segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. Centroid – The point.

Section 6.6 Concurrence of Lines

Medians and Altitudes of Triangles

5.3 Concurrent Lines, Medians, and Altitudes

Perpendiculars and Bisectors

DO NOW Complete the 4 problems at the top of your worksheet.

Bisectors, Medians, and Altitudes

Warm Up– in your notebook

Lesson 14.3 The Concurrence Theorems

5-2 Medians and Altitudes of Triangles

concurrency that we will be discussing today.

Presentation transcript:

5.3 Concurrent Lines, Medians, and Altitudes Stand Stand 0_23456789 Can you figure out the puzzle below??? No one understands!

Learning Target… To identify properties of perpendicular bisectors and angle bisectors, medians, and altitudes. Purpose: To be able to find locations in a park to place a fountain, statue, playground, etc.... 2

Definitions Concurrent Lines: Three or more lines that meet at one point. Point of Concurrency: The point at which concurrent lines meet. l m n P k 3

Properties of Bisectors Circumcenter of the Triangle: The point of concurrency of the perpendicular bisectors of a triangle. Theorem 5-6: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. 4

Properties of Bisectors Incenter of the Triangle: The point of concurrency of the angle bisectors of a triangle. Theorem 5-7: The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. 5

Definitions Median of a Triangle: A segments whose endpoints are a vertex and the midpoint of the opposite side. Altitude of a Triangle: Perpendicular segment from a vertex to the line containing the opposite side.

Properties of Medians Centroid of a Triangle: The point of concurrency of the medians of a triangle. Theorem 5-8: The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite sides. 7

Properties of Medians In the figure below, DE = 6 and AD = 16. Find DB and AF. F 8

Properties of Altitudes Orthocenter of a Triangle: The point of concurrency of the lines containing the altitudes of a triangle. Theorem 5-9: The lines that contain the altitudes of a triangle are concurrent. 9

Sum It Up which is… Figure concurrent at.. circumcenter equidistant from vertices bisector bisector incenter equidistant from sides median centroid 2/3 distance from vertices to midpoint altitude orthocenter --------------------- 10

5.3 Concurrent Lines, Medians, and Altitudes KNEE LIGHT LIGHT Can you figure out the puzzle below??? HW 5.3: #8-9, 11-16, 19-22, 28 Neon Lights