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