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Geometry
In The
Real World
By:
Halie Erin
Vertical Angles

Vertical Angles are the angles opposite each other when two lines cross.
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https://www.google.com/webhp?sourceid=chromeinstant&ion=1&espv=2&es_th=1&ie=UTF8#q=vertical%20angles%20in%20the%20real%20world

This picture represent vertical angles because two angles are congruent, so the other two
are also congruent. They also add up to 360 degrees.
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Theorems, Postulates, and Conjectures
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2-7-2 Vertical Angles Theorem
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Vertical angles are congruent
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2-7-3 If two congruent angles are supplementary, then each angle is a right angle.
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1-1-1 Through any two points there is exactly one line.
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1-1-2 Through any three noncolinear points there is exactly one plane containing them.
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1-1-4 If two lines intersect, then they intersect at exactly one point.
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1-1-5 If two planes intersect, then they intersect at exactly one point.
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1-2-2 Segment addition postulate – If B is between A &C, then AB+BC=AC
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1-3-2 Angle Addition Postulate – If S is in the interior of <PQR, then m<PQS+ m<SQR= m<
PQR.
Acute Triangle
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A triangle that has all angles less than 90° (90° is a Right Angle)
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https://www.google.com/webhp?sourceid=chromeinstant&ion=1&espv=2&es_th=1&ie=UTF8#q=acute%20triangles%20in%20the%20real%20world
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This slice of pizza has at least one acute angle.
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4-3-2 The acute angles of a right triangle are complementary
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3-2-2 Alternate Interior Angles Theorem
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3-2-3 Alternate Exterior Angles Theorem

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If two parallel lines are cut by a transversal, then the pairs of alternate exterior
angles are congruent
3-2-4 Same Side Interior Angles Theorem


If two parallel lines are cut by a transversal, then the pairs of alternate interior
angles are congruent
If two parallel line are cut by a transversal, then the two pairs of alternate exterior
angles are congruent.
3-4-3 If two intersecting lines form a linear pair of congruent angles, then the
lines are perpendicular.
Obtuse Triangle

A triangle that has an angle greater than 90°

https://www.google.com/search?q=obtuse+triangles+in+the
+real+world&espv=2&biw=1920&bih=895&tbm=isch&tbo=u&
source=univ&sa=X&ei=72ysVJeaEcmgNuGTgIAB&ved=0CB0Q
sAQ

This picture represents an obtuse triangle because it has an
obtuse angle.
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3-2-1 Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of
corresponding angles are congruent.
Right Triangle
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A right triangle (American English) or rightangled triangle (British English) is a triangle in which
one angle is a right angle (that is, a 90-degree angle).
The relation between the sides and angles of a right
triangle is the basis for trigonometry.
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This picture represents a Right Triangle because it has
one right angle (90 degrees.
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https://www.google.com/webhp?sourceid=chromeinstant&ion=1&espv=2&es_th=1&ie=UTF8#q=right%20triangles%20in%20the%20real%20world

https://www.google.com/search?q=trigonometry+ratios
&espv=2&biw=1280&bih=621&source=lnms&tbm=isch&s
a=X&ei=TruuVIWWM8qWNr60gagF&sqi=2&pjf=1&ved=0C
AYQ_AUoAQ#imgdii=_&imgrc=MWxz00ZLtPGxBM%253A%
3BLhtb4CjvvT7hKM%3Bhttp%253A%252F%252Fmaths.nay
land.school.nz%252FYear_Junior%252FTriangles%252FIm
ages%252Fposter_images%252FY10_Tr8.jpg%3Bhttp%253
A%252F%252Fmaths.nayland.school.nz%252FYear_Junior
%252FTriangles%252F2_trig_side.htm%3B696%3B521

https://www.google.com/search?q=pythagorean+theor
em&es_sm=93&source=lnms&tbm=isch&sa=X&ei=RLuuV
PHfN8eagwSruoK4AQ&ved=0CAgQ_AUoAQ&biw=1280&bi
h=621#tbm=isch&q=pythagorean+theorem+formula
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1-6-1 Pythagorean Theorem in a right angle, the sum of the
squares of the lengths of the legs is equal to the square of the
length of the hypotenuse.
2-6-1 Linear Pair Theorem
If two angles form a linear pair, then they are
supplementary.
2-6-2 Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to
two congruent angles), then the two angles are congruent.
2-6-3 Right Angle Congruence Theorem
All right angles are congruent
2-6-4 Congruent Complements Theorem
If two angles are complementary to the same angle or to
two congruent angles), then the two angles are congruent.
Pythagorean Theorem
Equilateral Triangle
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In geometry, an equilateral triangle is a triangle in which all three sides are
equal. In traditional or Euclidean geometry, equilateral triangles are also
equiangular; that is, all three internal angles are also congruent to each other
and are each 90°

https://www.google.com/search?q=equilateral+triangle+in+the+real+world&e
spv=2&biw=1920&bih=895&source=lnms&tbm=isch&sa=X&ei=WG2sVPWuKcSggSHuoGACg&ved=0CAYQ_AUoAQ

This picture represent Equilateral Triangles because all the sides and angles
are the same (congruent).
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Angles Bisector Theorem
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
If a point is on the bisector of an angle, then it is equidistant from the sides of the
angle.
8-1-1 The altitude to the hypotenuse of a right triangle forms two triangles
that are similar to each other and to the original triangle.
Isosceles Triangle
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A triangle with two equal sides; the angles opposite the equal
sides are also equal

https://www.google.com/search?q=isosceles+triangle+in+the+
real+world&espv=2&biw=1920&bih=895&tbm=isch&tbo=u&sou
rce=univ&sa=X&ei=622sVImgIIHcggSS_YPgCg&ved=0CCcQsAQ

This picture represents Isosceles Triangles because at least 2
sides have the same length (congruent).
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4-9-1 Isosceles Triangle Theorem
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If two sides of a triangle are congruent, then the angles opposite
the sides are congruent.
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4-9-3 If a triangle is equilateral, then it is equiangular.
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4-9-4 If a triangle is equiangular, then it is equilateral.
Scalene Triangle
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A triangle with all sides of different lengths.
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No sides are equal and no angles are equal.

https://www.google.com/search?q=scalene+triangle+in+the+real+
world&espv=2&biw=1920&bih=895&tbm=isch&tbo=u&source=univ
&sa=X&ei=IW6sVKGhF4KrgwSO5IKwDg&ved=0CB0QsAQ

This picture represent Scalene Triangle because none of the sides
or angles are congruent.
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3-5-1 Parallel Lines Theorem
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In a coordinate plane, two nonvertical lines are parallel if and only if
they have the same slope. Any two vertical lines are parallel.
3-5-2 Perpendicular Lines Theorem
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In a coordinate plane, two nonvertical lines are perpendicular if and
only if the product of their slopes is -1. Vertical and horizontal lines
are perpendicular
Circle with a Tangent
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This picture has Skittles and there's a tangent when you line them up like
this.
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A tangent on a circle is a straight line on the edge of the circle.

https://www.google.com/search?q=circle+with+tangent+in+the+real+world&e
spv=2&biw=1280&bih=621&source=lnms&tbm=isch&sa=X&ei=D72uVKrBBYqaNq
XAgLgL&ved=0CAYQ_AUoAQ#imgdii=_
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4-3-1 Triangle Sum Theorem
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The sum of the angle measures of a triangle is 180 degrees