Unique Triangles

Triangle Inequality Theorem

Determining Triangles

Multiple Choice

If the longest side of the triangle was 10. Then the two shorter sides must have a sum that is ....?

• any length

• equal to 10

• greater than 10

• less than 10

Multiple Choice

Which set of numbers may represent the lengths of the sides of a triangle?

• {2,5,9}
• {6,6,7}
• {6,4,2}           
• {7,8,1}

Multiple Choice

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6?

• 6

• 7

• 5

• 4

Multiple Choice

Can the sides of a triangle have lengths 3, 4, and 9?

• Yes

• No

• I don't know

• Cannot be determined

Multiple Choice

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

• I don't know.

• Cannot be determined

Watch the video on the next slide

• Take notes

• Answer the questions that follow

What makes a Unique Triangle?

• Given ALL 3 sides

• Given 2 sides and an angle in between

• Given 2 angles and 1 side in between

• Given 2 angles and 1 side opposite of the angles

What makes multiple triangles?

• Given 3 angles (must add up to 180)

• Given 2 sides and an angle but the angle does NOT have to be between the sides.

• Given 2 angles and a side but the side does NOT have to be between or across from the angles

Multiple Choice

How many triangles can be created when you know two angles and one non-included side?

• Only 1 unique triangle

• multiple triangles

• no triangles

Multiple Choice

In this triangle, if angle A is 45 degrees, angle C is 45 degrees, and line AB is 5 cm, how many triangles can you create?

• one unique triangle

• multiple triangles

• no triangles

Multiple Choice

Two angles of a triangle measure 30° and 108°. What is the measure of the third angle of the triangle?

• 42
• 45
• 62

Multiple Choice

How many triangles can be created when you know two sides and one non-included angle?

• Only 1 unique triangle

• multiple triangles

• no triangles

Multiple Choice

How many triangles exist with the following angle measures?

100°, 100°, 50°

• No triangle exists with the given angle measures.

• More than one triangle exists with the given angle measures.

• Exactly one unique triangle exists with the given angle measures.

Multiple Choice

How many triangles can be created when you know two angles and 1 included side?

• Only 1 unique triangle

• multiple triangles

• no triangles

Multiple Choice

How many triangles can be created with the side lengths of 3 cm, 4cm, and 5 cm?

• Only 1 unique triangle

• multiple triangles

• no triangles

Multiple Choice

Given three angle measures, how many triangles can you create?

• One unique triangle

• Multiple triangles

• No triangles