Review of Triangles

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Review of Triangles

• SPI 3108.4.3      Identify, describe and/or apply
  the relationships and theorems involving
  different types of triangles, quadrilaterals and
  other polygons.

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Triangles

• A triangle is a figure formed by three
  noncollinear points connected by three segments.
  All triangles can be classified by its side and
  by its angle.

C
a
b
A
B
c
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Acute Triangles

• An acute triangle is a triangle with all acute
  angles. An acute triangle has three angles each
  less than 90 degrees.

80
50
50
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Obtuse Triangles

• An obtuse triangle is a triangle with one obtuse
  angle (greater than 90 degrees) and two acute
  angles.

40
110
30
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Right Triangles
45

• A right triangle is a triangle with one right
  angle (equal to 90 degrees) and two acute angles.

90
45
6
Scalene Triangles

• A scale triangle is a triangle with three unequal
  sides.

12
9
18
7
Isosceles Triangles

• An isosceles triangle is a triangle with (at
  least) two equal sides.

14
14
12
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Isosceles Triangle Theorem

• The Isosceles Triangle Theorem states if two
  sides of a triangle are congruent, then the
  angles opposite those sides are congruent.

14
14
12
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Equilateral Triangles

• An equilateral triangle is a triangle with all
  three sides of equal length. Since all three
  sides are equal therefore, all three angles are
  equal also.

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Parts of Right Triangles

• A right triangle has two legs and an hypotenuse.
  The hypotenuse is the side opposite of the right
  angle. The other two sides are called legs.

Hypotenuse
Leg
Leg
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The Pythagorean Theorem

• For a right triangle with legs a and b and
  hypotenuse c, a2 b2 c2.

c
a
b
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Triangle Quiz

• Please complete the following quiz that covers
  the information that was just presented to you.

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Question 1

• If a triangle has three unequal sides it is a
  ______ triangle.
• A) Scalene
• B) Obtuse
• C) Isosceles

• Answer
• A) Scalene

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Question 2

• A triangle with (at least) two equal sides is a
  ______ triangle.
• A) Scalene
• B) Isosceles
• C) Congruent

• Answer
• B) Isosceles

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Question 3

• A triangle with all three sides of equal length
  is a ______ triangle.
• A) Equilateral
• B) Right
• C) Equiangular

• Answer
• A) Equilateral

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Question 4

• A triangle with an angle of 90 is a ______
  triangle.
• A) Acute
• B) Right
• C) Congruent

• Answer
• B) Right

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Question 5

• A triangle in which all three angles are less
  than 90 is a ______ triangle.
• A) Right
• B) Acute
• C) Scalene

• Answer
• B) Acute

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Question 6

• A triangle in which one of the angles is greater
  than 90 is a ______ triangle.
• A) Obtuse
• B) Isosceles
• C) Acute

• Answer
• A) Obtuse

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Question 7

• What is the Hypotenuse of a right triangle?
• A) The smallest angle.
• B) The side opposite the right angle.
• C) The right angle.

• Answer
• B) The side opposite the right angle.

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Question 8

• The Pythagorean Theorem states
• A) pr2
• B) (ab)2/2c
• C) a2b2c2

• Answer
• C) a2b2c2

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Question 9

• Use the Pythagorean Theorem to solve the
  following
• a 5
• b 12
• c ?

• Answer
• c 13

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Question 10

• Use the Pythagorean Theorem to solve the
  following
• a ?
• b 16
• c 20

• Answer
• a 12