TODAY IN GEOMETRY…

Warm up: Calculate midsegments

Learning Target: 5.4 Identify the Medians of Triangles and the Centroid

Independent Practice

Mini Quiz – Friday! ALL HW due Friday!

𝑅 𝑆

𝐽

Complete the statement:

1.

2.

3.

4.

5.

6.

𝐿𝑇

𝐾WARM UP:

𝐽𝐿

𝐽𝐾

𝑅𝑇

𝑅𝑇𝐾𝑆

𝑆𝑇𝐾𝑅

𝑅𝑆𝐿𝑇

MEDIAN OF A TRIANGLE: A segment from a vertex to the midpoint of the opposite side.

vertex

midpointm

edian

Find the midpoint on one segment.

Draw a line from the opposite vertex through the midpoint.

The three medians of a triangle are concurrent. The point of concurrency is called the CENTROID and falls inside the circle. The centroid is the balancing point of a triangle.

Find the medians for each side of the triangle.

CENTRIOD

CONCURRENCY OF MEDIANS: The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

𝐴

CENTRIOD

𝑃

𝐵

𝐴𝑃=23𝐴𝐵

A different way to think about this:

is twice as long as OR

is half of

𝟐 𝒙

𝒙

PRACTICE: is the centroid of ,

𝐷

𝐴

𝑃

𝐵

𝐶

𝐸

𝐹

12

6

1.

2.

3.

4.

5.

6.

𝐴𝐹=1213𝐶𝐸=9

23𝐶𝐸=18

12𝐷𝑃=3

𝐹 𝑃+𝑃𝐷=9

2 𝐴𝐹=24

PRACTICE: is the centroid of . Find x.

𝐴

𝐵

𝐺

𝐷

𝐸

𝐶

𝐹

1. 2.

𝟓=𝒙

PRACTICE: Find the midpoint of then draw the median. Use the median to find the coordinates of the centroid.

Midpoint Formula

Substitute Values

Add and Divide

Connect the midpoint to vertex

Centroid is

Count 6 units down from the vertex

Centroid is 𝑀 (7 4)

𝟗𝐴(3 ,7)

𝐸 (11 ,1)

𝐶 (7 ,13)

(7 ,7)

HOMEWORK #2:

Pg. 322: 3-11, 33-35

If finished, work on other assignments:

HW #1: Pg. 298: 3-15, 24-27