Triangles

Classifying Triangles

How do I identify a triangle by its sides?

How do I identify a triangle by its angles?

​

​

​

Multiple Choice

What type of angle is this?

• acute

• right

• obtuse

Multiple Choice

What type of angle is this?

• acute

• right

• obtuse

Multiple Choice

What type of angle is this?

• acute

• right

• obtuse

Key Idea #1

We can name triangles based on their angles:

• All the angles of ACUTE triangles are less than 90 degrees.

• A RIGHT triangle had one angle that is 90 degrees.

• An OBTUSE triangle has one angle greater than 90 degrees.

Multiple Choice

A triangle where all of the angles are less than 90 degrees is called a(n)

• equilateral triangle

• acute triangle

• obtuse triangle

• right triangle

Multiple Choice

A triangle where one angle is greater than 90 degrees is called a(n)

• equilateral triangle

• obtuse triangle

• isosceles triangle

• scalene triangle

Fill in the Blank

A triangle where one angle is 90 degrees is called a(n)

Key Idea #2

Triangles can be identified by their sides.

• Equilateral Triangle: all sides are the same length.

• Isosceles Triangles: two sides are the same length

• Scalene Triangle: no sides are the same length.

Multiple Choice

A triangle where all two sides are the same length is called

• equilateral triangle

• obtuse triangle

• isosceles triangle

• scalene triangle

Multiple Choice

A triangle where all three sides are of UNEQUAL length is called

• equilateral triangle

• obtuse triangle

• isosceles triangle

• scalene triangle

Multiple Choice

A triangle where all three sides are the same length is called

• equilateral triangle

• obtuse triangle

• isosceles triangle

• scalene triangle

Key Idea #3

Each angle of a triangle has a side that is OPPOSITE that angle.

Key Idea #4

The LONGEST side of a triangle is OPPOSITE the LARGEST angle.

Which side is the longest?

​Side AC

Key Idea #5

The SHORTEST side of a triangle is OPPOSITE the SMALLEST angle.

​Side AB

Key Idea #6

If two angles in a triangle have the SAME MEASURE, then the side opposite those angles have the SAME LENGTH. Which two sides have the same length?

​Side AB, AC

Key Idea #7

A regular triangle is called an EQUILATERAL triangle.

What makes it a regular triangle?

It has sides that are all the same length and angles all the same measure

Fill in the Blank

Each angle of a triangle has a side that is ________ that angle.

Fill in the Blank

The LONGEST side of a triangle is OPPOSITE the ________ angle.

Fill in the Blank

The _______ side of a triangle is OPPOSITE the smallest angle.

Fill in the Blank

If two angles in a triangle have the ____ _______, then the side opposite those angles have the SAME LENGTH.

Multiple Choice

Do you think a triangle can be formed with the following side lengths?

4, 7, 10

• yes

• no

Multiple Choice

Do you think a triangle can be formed with the following side lengths?

10, 12, 23

• yes

• no

If we know two sides of a triangle, we can find a range of possible lengths for the third side.

• ADD the two given sides to get the MAXIMUM length of the third side.

• SUBTRACT the two given sides to get the MINIMUM length of the third side.

The two given sides of a triangle are 6 and 9. What could the third side be?

Consider that the 6 and 9 could be the 2 larger sides OR the 6 and 9 could be the 2 smaller sides.

Open Ended

Name a possible length for the third side of a triangle with sides 4 and 7.

Open Ended

Name a possible length for the third side of a triangle with sides 11 and 19.

The Pythagorean Theorem

A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the

equation a² + b² = c².

What are they?

Pythagorean Triples

​Pythagorean Inequality Theorem

Multiple Choice

Which type of triangle will be created if you use side lengths 6, 8, and 9?

• right

• obtuse

• acute

Multiple Choice

Which type of triangle will be created if you use side lengths 6, 8, and 10?

• right

• obtuse

• acute

Angle Sum & Exterior Angle Theorems of Triangles

Fill in the Blank

Solve for x.

Solve for x.

• 7x - 11 + 5x - 2 + 2x - 3 = 180

• 14x - 16 = 180

• 14x = 196

• x = 14

Angle Relationships in Triangles

Holt Geometry

Holt McDougal Geometry

An auxiliary line is a line that is added to a figure
to aid in a proof.

An auxiliary line

used in the

Triangle Sum

Theorem

All angles that form a straight line add up to 180°

An auxiliary line

used in the

Triangle Sum

Theorem

The interior is the set of all points inside the
figure. The exterior is the set of all points
outside the figure.

Interior

Exterior

An interior angle is formed by two sides of a
triangle. An exterior angle is formed by one
side of the triangle and extension of an adjacent
side.

∠4 is an exterior angle.

∠3 is an interior angle.

Interior

Exterior

Multiple Choice

What is the value of the missing angle?

• 90

• 100

• 20

• 120

Multiple Choice

What is the value of the missing angle?

• 105

• 80

• 55

• 25

Each exterior angle has two remote interior angles. A
remote interior angle is an interior angle that is not
adjacent to the exterior angle.

Exterior

∠4 is an
exterior angle.

The remote
interior angles
of ∠4 are ∠1
and ∠2.

Multiple Choice

Find the measure of each angle indicated.

• $$70\degree$$

• $$170\degree$$

• $$10\degree$$

• $$40\degree$$

Multiple Choice

What is the measure of angle x?

• 70

• 160

• 135

• 20