WARM UP March 11, 2014

WARM UP March 11, 20141. Solve for x2. Solve for y

(40 + y)° 28°

3xº xº

EOCT Week 9 #2

Medians of a TriangleThe MEDIANS of a triangle join the vertex of one angle to the opposite side’s midpoint.

Every Triangle has 3 Medians.

The intersection of the medians is called the CENTROID.

Centroid Theorem

The length of the segment from the vertex to the

centroid is twice the length of the segment from the centroid to the midpoint.

A BF

WE

C

D

A BF

WE

C

D

How do you find the Centroid Given 3 points?Remember the midpoint formula, )

The Centroid Formula is very similar., )

ExampleFind the centroid of a triangle whose vertices are (-1, -3), (2, 1) and (8, -4).

You Try!!Find the centroid of a triangle whose vertices are A(4, -1), B(2, 6), and C(9, -5).

In ABC, AN, BP, and CM are medians.

A

B

M

P E

C

N

If EN = 12, find AN.AE = 2(12)=24

YOU TRY!!!!

AN = 36

AN = AE + ENAN = 24 + 12

Mid-Segment of a TriangleThe MID-SEGMENT of a triangle is a segment that joins two midpoints of two sides of a triangle.

The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle.

EXAMPLES

Triangle Proportionality Theorem If a line is parallel to one side of the triangle and it intersects the other two sides, then the line divides the other two sides proportionally.

ExamplesSolve for x.

9 = 3x3 = x

YOU TRY!!

Solve for x.