for the following problems, use a(0,10), b(24,0), c(0,0) find ab find the midpoint of ca find the...

BellworkFor the following problems, use

A(0,10), B(24,0), C(0,0)•Find AB•Find the midpoint of CA•Find the midpoint of AB•Find the slope of AB

Bellwork SolutionFor the following problems, use A(0,10), B(24,0), C(0,0)•Find AB

2 2

2 2

(10 0) (0 24)

10 ( 24)

100 576

676 26

d

d

d

d

Bellwork SolutionFor the following problems, use A(0,10), B(24,0), C(0,0)•Find the midpoint of CA

0 0 10 0,

2 2

0 10,2 2

0,5

Bellwork SolutionFor the following problems, use A(0,10), B(24,0), C(0,0)•Find the midpoint of AB

0 24 10 0,

2 2

24 10,

2 2

12,5

Bellwork SolutionFor the following problems, use A(0,10), B(24,0), C(0,0)•Find the slope of AB

10 0

0 2410 5

24 12

Midpoint Theorem and Coordinate Proof

Section 5.1

The ConceptThis chapter covers some very important theorems and

properties of trianglesThese theories will aid us in our introductory

exploration of trigonometry in Chapter 7

TheoremTheorem 5.1: Midsegment TheoremThe segment connecting the midpoints of two sides of a triangle

is parallel to the third side and is half as long as that side

midpoint midpointHow could we show this?

A

A B

B

Example

ExampleFind AB, if A & B are midpoints

3x+8

2x+24

A

G J

B6 16 2 24x x 2(3 8) 2 24x x

4 16 24x 4 8x

2x

DefinitionCoordinate Proof

Process of placing a geometric figure on the coordinate plane and then using variables to represent the coordinates to prove various statements

Y

X

Y

X(2k,0)

(k,h)

Example

Homework

5.1 Exercises

1-11, 12-18 even, 24-28 even, 33-39 odd

ExampleHow many feet of steel is needed to complete the triangular portion of the structure.

Y

X

Y

X

ExampleProve that Triangle PQR is isosceles

Q (-h,0) R (h,0)

P (0,k)

Most Important Points• Midpoint Theorem• Placing a geometric figure on the coordinate plane