dr. fowler ccm1a exam review 01. pythagorean theorem leg hypotenuse the hypotenuse is always the...
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Dr. Fowler CCM1A
EXAM REVIEW 01
Pythagorean Theorem
leg
leg
hypotenuse
The hypotenuse is always the longest side of a right triangle and is always opposite the right angle.
Using aUsing a22 + b + b22 = c = c22
Looking for length ofLooking for length of
the hypotenusethe hypotenuse aa22 + b + b22 = c = c22
151522 + 20 + 2022 = c = c22
225 + 400 = c225 + 400 = c22
625 = c625 = c22
625 c2
25 c
Using aUsing a22 + b + b22 = c = c22
Find the LegFind the Leg aa22 + b + b22 = c = c22
6622 + b + b22 = 10 = 1022
36 + b36 + b22 = 100 = 100 -36 -36-36 -36 bb22 = 64 = 64 b = 8b = 8
Ex 1Find the distance between the points P(-3, 2) and Q (-2, 4).
1, 1( )x y 2, 2( )x y
2 22 1 2 1( ) ( )d x x y y
2 2( ) ( )d 2 3 24
2 2( ) ( )d 1 2
d 1 4
5 d
Work inside parentheses
Do powers before doing the addition!!!!!!
+ 4 + 4
3 · · 3
x = 36
12 – 4 = 8
123
x
2) Solve 4 83
x
1. Draw “the river”2. Add 4 to both
sides3. Simplify4. Clear the fraction -
Multiply both sides by 3
5. Simplify6. Check your
answer
D U
÷ 3- 4
+ 4· 3
364 8
3
3) Solve d 4
23
d – 4 = 6
+ 4 + 4
d = 10
1. Draw “the river”2. Clear the fraction -
Multiply both sides by 2
3. Simplify4. Add 4 to both sides5. Simplify6. Check your answer
D U
- 4÷ 2
· 2+ 4
42 3 2
2
d
10 43
2
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Solve With x’s on Both Sides 7x 5 3x 23
3x 3x 4x 5 23
5 5 4x 284 4
x 7
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13 = 4(3x – 7) + 5
13 = 12x - 28 + 5
13 = 12x - 23 +23 +23
36 = 12x__ ___ 12 12
3 = x
13 = 4(3 3 – 7) +5
13 = 4(9 - 7) + 5
13 = 8 + 5
13 = 13
13 = 4(2) + 5
Solve With The Distributive Property
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3y 6(y 2) 24 3y 6y 12 24
9y 12 24 12 12 9y 369 9
y 4
Solve With The Distributive Property
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2(3x 1) 4(10 2x)
8x 8x 14x 2 40
2 2 14x 4214 14
x 3
6x 2 40 8x
Solve With The Distributive PropertyChallenging One!
Excellent Job !!!Well Done
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