Download Geometry

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Acute angles are < 900
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Obtuse angles are > 900
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Right angles are = 900
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Supplementary angles total to 1800.
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Complementary angles total to 900.
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If two angles are complementary and one is 2
times greater than the other, what is the
measure of the smaller angle and what type
of angle is it?
X = smaller angle 2x = larger angle
Equation: x + 2x = 90
 3x = 90
 X = 30 and the angle is
acute
1
2
3
4
5
6
7
8
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Vertical angles are congruent 1&4, 2&3, 5&8, 6&7
Alternate interior angles are congruent 3&6, 4&5
Alternate exterior angles are congruent 1&8, 2&7
Corresponding angles are congruent 1&5, 3&7, 2&6, 4&8
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Same side interior angles are supplementary
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3&5, 4&6
If <1 = 2x+3 and <5=x+7
What is the value of x?
1
2
4
3
5
2x-3 = x+7
X= 10
8
6
7
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The sum of the angles of a triangle is 180°.
Isosceles triangle – 2 sides and base angles
congruent
Equilateral triangle – all sides and angles
congruent
The sum of the two remote interior angles =
the value of the exterior angle
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In a triangle the second angle is 2 time the
first angle. The third angle is 5 more than
the second angle. Find the measure of each
angle.
2x
x
X + 2x + (2x +5) = 180
5x + 5 = 180
7x =
2x+5
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Only works with a RIGHT triangle
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SIDE2 + SIDE2 = HYPOTENUSE2
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a2
+ b2
=
c2
But Implies:
if a2 + b2 > c2 C is an acute angle (<90°)
if a2 + b2 < c2 C is an obtuse angle (>90°)
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Parallelogram –
◦ opposite sides are parallel and congruent
◦ Opposite angles are =
◦ The diagonals bisect each other
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Rectangle – a parallelogram with right angles
Square – a rectangle with all sides equal
Trapezoid: has one pair of parallel sides
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The Sum of the angles of a polygon = 180(n-2)
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What is the sum of the angles of a hexagon:
180(6-2)==720
12
Side-Side-Side
Angle-Side-Angle
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Side-Angle-Side
When trying to prove
that two triangles are
congruent, use
matching parts and
figure out which
congruence postulate
to use!
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If triangles are similar, the sides are in
proportion and so are the perimeters
4 x

12 9
36  12 x
3 x
4
2
x
6
12
9
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r= radius d= Diameter
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2r=d
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Circumference: C = 2Πr
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Area = A = Πr2
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Circles contain 360°
1.
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Find the area of a circle with diameter = 12 “
A.
B.
C.
D.
144Π
36 Π
12 Π
6Π
The correct answer is B
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Central Angle – angle formed by two rays
extending from the center
Central Angle Arc Area of Sector


360
C
A
Find the length of the arc intercepted by a
30 degree angle in a circle with radius = 4.
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30
arc

360 2r
30 arc

360 8
arc = (30 x 8Π) / 360
2
arc =
3
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Inscribed angles have their vertex on the
circle and the intercepted are =
½ the measure of the angle
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Inscribed – inside an object
◦ The circle is inscribed by the square
 It just touches the edges
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Circumscribed – surrounding an object
◦ The circle circumscribed the square
 It just touches the edges