Applying Triangle Sum Properties Section 4.1. Triangles Triangles are polygons with three sides. ...
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Transcript of Applying Triangle Sum Properties Section 4.1. Triangles Triangles are polygons with three sides. ...
![Page 1: Applying Triangle Sum Properties Section 4.1. Triangles Triangles are polygons with three sides. There are several types of triangle: Scalene](https://reader036.fdocuments.us/reader036/viewer/2022062304/56649d9f5503460f94a89aab/html5/thumbnails/1.jpg)
Applying Triangle Sum Properties
Section 4.1
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Triangles Triangles are polygons with three sides.
There are several types of triangle: Scalene Isosceles Equilateral Equiangular Obtuse Acute Right
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Scalene Triangles Scalene triangles do not have any congruent
sides.
In other words, no side has the same length.
3cm
8cm
6cm
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Isosceles Triangle A triangle with 2 congruent sides.
2 sides of the triangle will have the same length.
2 of the angles will also have the same angle measure.
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Equilateral Triangles All sides have the same length
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Equiangular Triangles All angles have the same angle measure.
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Obtuse Angle Will have one obtuse angle.
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Acute Triangle All angles are acute angles.
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Right Triangle Will have one right angle.
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Exterior Angles vs. Interior Angles Exterior Angles are angles that are on the
outside of a figure.
Interior Angles are angles on the inside of a figure.
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Interior or Exterior?
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Interior or Exterior?
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Interior or Exterior?
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Triangle Sum Theorem (Postulate Sheet) States that the sum of the interior angles is
180.
We will do algebraic problems using this theorem. The sum of the
angles is 180, so
x + 3x + 56= 1804x + 56= 180
4x = 124x = 31
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Find the Value for X
2x + 15
3x
2x + 15 + 3x + 90 = 180
5x + 105 = 180
5x = 75
x = 15
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Corollary to the Triangle Sum Theorem (Postulate Sheet) Acute angles of a right triangle are
complementary.
3x + 10
5x +16
3x + 10
20
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Exterior Angle Sum Theorem The measure of the exterior angle of a triangle is equal to
the sum of the non-adjacent interior angles of the triangle
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88 + 70 = y
158 = y
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2x + 40 = x + 72
2x = x + 32 x = 32
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Find x and y
3x + 13
46o
8x - 1
2yo
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