Geometry 5-3 Medians and Altitudes A median of a triangle: a segment from the midpoint of a side to the opposite angle. Centroid: where all 3 medians intersect.

Slides:

Advertisements

Similar presentations

Advertisements

Date: Sec 5-4 Concept: Medians and Altitudes of a Triangle

Aim: How do you construct the 9-point circle? Do now: What is the orthocenter? The orthocenter of a triangle is the point where the three altitudes meet.

4.6 Medians of a Triangle.

3.7—Medians and Altitudes of a Triangle Warm Up 1. What is the name of the point where the angle bisectors of a triangle intersect? Find the midpoint of.

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

Honors Geometry Section 4.6 Special Segments in Triangles

Unit 4 Vocabulary. Midsegment Segments connecting the midpoints of triangles Creates 4 congruent triangles within the triangle.

5-3: Medians and Altitudes Medians and Altitudes in a Triangle

Finding Equations of Lines If you know the slope and one point on a line you can use the point-slope form of a line to find the equation. If you know the.

Warm-Up Find the area of each triangle

Median and Altitude of a Triangle Sec 5.3

Points of Concurrency Triangles.

Special Segments of Triangles

Lesson 12 – Points of Concurrency II

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.

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

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

Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4.

5.4 – Use Medians and Altitudes Length of segment from vertex to midpoint of opposite side AD =BF =CE = Length of segment from vertex to P AP =BP =CP =

Chapter 5: Relationships in Triangles. Lesson 5.1 Bisectors, Medians, and Altitudes.

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

SPECIAL SEGMENTS OF TRIANGLES SECTIONS 5.2, 5.3, 5.4.

Warm Up Announcements  Test Friday  Homework: TEXAS Practice Test Pg. 194.

Points of Concurrency MM1G3e Students will be able to find and use points of concurrency in triangles.

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

Triangles are cool! What is a perpendicular bisector in a triangle? What is a median in a triangle? goes through the midpoint and is perpendicular to.

MEDIANS AND ALTITUDES SECTION 5.4. MEDIANS OF A TRIANGLE A median of a triangle is a segment from a vertex to the midpoint of the opposite side.

The intersection of the medians is called the CENTROID. How many medians does a triangle have?

5.3 Medians and Altitudes CentroidOrthocenter. Definition of a Median A median is a segment from a vertex of a triangle to the midpoint of its opposite.

Ch. 5 – Properties of Triangles

5-2 Median & Altitudes of Triangles

Warm Up Week 7. Geometry 5.3 Day 1 I will use properties of medians of a triangle. A segment with endpoints on a vertex and the midpoint of the.

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

Bellwork 1)If, what is ? 2)If, what is ? 3)If, what is ? What is x?

Do Now 1. For A(–4, 8) and B(5, 8), find the midpoint of AB.

Use Medians and Altitudes

Medians Median vertex to midpoint.

Use Medians and Altitudes

5-4 Medians and Altitudes

In your journal: Medians and Altitudes

Medians, Altitudes and Perpendicular Bisectors

Special Segments in a Triangle

Triangle Centers Points of Concurrency

Perpendicular Bisector

A median of a triangle is a segment whose endpoints are

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

Medians & Altitudes of Triangles

Vocabulary and Examples

Special Segments in Triangles

Centers of Triangles or Points of Concurrency

Geometry 5.2 Medians and Altitudes of a Triangle

Bisectors, Medians and Altitudes

5-4 Medians and Altitudes

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.

8.3 Medians and Altitudes of Triangles

Warm Up 5.1 skills check!. Warm Up 5.1 skills check!

5.3 Concurrent Lines, Medians, and Altitudes

5.4 Medians and Altitudes Mrs. Vazquez Geometry.

MID-TERM STUFF HONORS GEOMETRY.

A median of a triangle is a segment whose endpoints are

Warm Up– in your notebook

Medians and Altitudes of Triangles

Altitude, perpendicular bisector, both, or neither?

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.

concurrency that we will be discussing today.

Presentation transcript:

Geometry 5-3 Medians and Altitudes A median of a triangle: a segment from the midpoint of a side to the opposite angle. Centroid: where all 3 medians intersect

Finding the Centroid The centroid splits a median into 1/3 and 2/3 parts A B C X Y Z P 30 ÷ 3 = 10 AP = 20 XP = 10 If AX = ÷ 2 = 6 PZ = 6 CZ = = 18 If CP = 12 PB = 18 BY = 27 If YP = 9

Examples Segment AE is a median for ΔABC. If BE = 3x – 5 and CE = x + 1, what is the length of BC? A B C E BE = CE 3x – 5 = x + 1 -x -x 2x – 5 = x = 6 x = 3 BE = 3(3) – 5 = 4 BC = 8

Altitude An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. The altitude of a triangle is the height you would use for the area of a triangle: A = (1/2)bh Orthocenter: where the 3 altitudes intersect

Orthocenter The orthocenter of a triangle is where all three altitudes meet. orthocenter