For the following problems, use A(0,10), B(24,0), C(0,0) Find AB Find the midpoint of CA Find the...
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Transcript of For the following problems, use A(0,10), B(24,0), C(0,0) Find AB Find the midpoint of CA Find the...
![Page 1: For 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.](https://reader037.fdocuments.net/reader037/viewer/2022103122/56649d015503460f949d369e/html5/thumbnails/1.jpg)
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
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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
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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
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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
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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
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Midpoint Theorem and Coordinate Proof
Section 5.1
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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
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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
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Example
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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
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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)
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Example
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Homework
5.1 Exercises
1-11, 12-18 even, 24-28 even, 33-39 odd
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ExampleHow many feet of steel is needed to complete the triangular portion of the structure.
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Y
X
Y
X
ExampleProve that Triangle PQR is isosceles
Q (-h,0) R (h,0)
P (0,k)
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Most Important Points• Midpoint Theorem• Placing a geometric figure on the coordinate plane