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Pythagorean Theorem In a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. (“c” is always the.

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Presentation on theme: "Pythagorean Theorem In a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. (“c” is always the."— Presentation transcript:

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2 Pythagorean Theorem In a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. (“c” is always the hypotenuse) a b c (leg) (hyp)

3 Distance Formula Where d stands for distance x 1 & y 1 are one endpoint of a segment x 2 & y 2 are the second endpoint of a segment (x 1, y 1 ) (x 2, y 2 ) d

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5 What do you say when you walk into a cold room? It’s collinear! (It’s cold in here!)

6 Midpoint of a Segment The point halfway between the endpoints of a segment If X is the midpoint of Segment AB, then A B X (the measure of AX = the measure of XB)

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8 Midpoint Formula On a Single Number Line: On a Double Number Line (Coordinate Plane): A B -3 7 X 2 5 Units x y (5,5) (-3,- 1) (x 1,y 1 ) (x 2,y 2 ) (1,2 )

9 (a single number line) M

10 (a double number line) M(2.5, 1.5) (Not to scale)

11 Find the Coordinates of an Endpoint The Midpoint Formula can be used to find the coordinates of an endpoint when the midpoint and one endpoint are given. Find the coordinates of Endpoint B, if M = 5 is the midpoint, and A = -12 is the other endpoint. Multiply both sides by 2 Solve for B A -12 M 5 B ? units (a single number line)

12 Let X = (x 1,y 1 ) (One endpoint) Y = (-2, 2) (Midpoint) Z = (2, 8) (Other endpoint) (x 2, y 2 ) (x, y) X(?) Y (-2,2) Z (2, 8) (x, y) (x 2, y 2 ) (x 1, y 1 ) (The midpoint is always the ordered pair with no subscripts) (-4, -6)

13 Look for an equation to write, then solve: -2x +5 Does it work? ? ? Be sure to answer the question.

14 Freebies

15 HW: Page 25 (3 – 45 odds)


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