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Triangle Properties

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Classifying Triangles

Triangles Classified by Angles

60°

80°

40°

acute

triangle

3^rd angle is

_____

acute

obtuse

triangle

right

triangle

3^rd angle is

______

obtuse

3^rd angle is

____

right

17°

43°

120°

30°

60°

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Classifying Triangles

Triangles Classified by Sides

scalene

isosceles

equilateral

no

___

sides

congruent

__________

sides

congruent

___

sides

congruent

at least two

all

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Isosceles Triangles

You will learn to identify and use properties of _______

triangles.

1) _____________

2) ____

3) ____

isosceles

isosceles triangle

base

legs

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Isosceles Triangles

Recall from §5-1 that an isosceles triangle has at least two congruent sides.

The congruent sides are called ____.

legs

The side opposite the vertex angle is called the ____.

base

In an isosceles triangle, there are two base angles, the vertices where the

base intersects the congruent sides.

vertex angle

leg

base

base angle

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Angles of a Triangle

You will learn to use the Angle Sum Theorem.

1) On a piece of paper, draw a triangle.

2) Place a dot close to the center (interior) of the triangle.

3) After marking all of the angles, tear the triangle into three pieces.

then lay them so that the 3 marked angles make a line.

4) Make a conjecture about the sum of the angle measures of the triangle.

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Triangle Sum Theorem

Theorem 5-1 Triangle Sum Theorem

The sum of the measures of the angles of a triangle is 180.

z°

x°

y°

x + y + z = 180

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Triangle Inequalities

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Triangle Inequality Theorem:

The sum of the lengths of the 2 smaller sides of a triangle are greater than the length of the third side.

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a + b > c

Example:

Determine if it is possible to draw a triangle with side measures 12, 11, and 17.

12 + 11 > 17 → Yes

Therefore a triangle can be drawn.

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Finding the range of the third side:

Since the third side cannot be larger than the other two added together, we find the maximum value by adding the two sides.

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Since the third side and the smallest side cannot be larger than the other side, we find the minimum value by subtracting the two sides.

Example:

Given a triangle with sides of length 3 and 8, find the range of possible values for the third side.

The maximum value (if x is the largest side of the triangle) 3 + 8 > x

11 > x

The minimum value (if x is not that largest side of the ∆) 8 – 3 < x

5< x

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Ex. 4: Finding Possible Side Lengths

A triangle has one side of 10 cm and another of 14 cm. Describe the possible lengths of the third side
SOLUTION: Let x represent the length of the third side. Using the Triangle Inequality, you can write and solve inequalities.

14 - 10 < x < 14 + 10

4 < x < 24

►So, the length of the third side must be greater than 4 cm and less than 24 cm.

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5. Geography

CG + MC> MG

99 + 165 > x

264 > x

x < 165 - 99

x < 66

66 < x < 264

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