Constructing Unique Triangles: Key Concepts and Methods

The video tutorial covers constructing triangles using the Triangle Sum Theorem and the Triangle Inequality Theorem. It explains how to determine the number of triangles that can be formed given three angle measures or three side lengths. The tutorial includes step-by-step instructions for constructing triangles with specific angles and discusses the conditions under which unique triangles can be formed. It also provides examples and exercises to reinforce the concepts.

What is the sum of the interior angles of any triangle?

• 180 degrees

• 360 degrees

• 270 degrees

• 90 degrees

What is the sum of angles for any triangle?

• 180 degrees

• 90 degrees

• 360 degrees

• 270 degrees

If two angles of a triangle are 40 degrees and 60 degrees, what is the measure of the third angle?

• 80 degrees

• 90 degrees

• 100 degrees

• 70 degrees

How many unique triangles can be formed with angles 40°, 60°, and 80°?

• Two

• Infinite

• One

• None

If a triangle has angles of 50°, 50°, and 100°, how many unique triangles can be formed?

• Two

• One

• None

• Infinite

According to the Triangle Inequality Theorem, can a triangle have sides of lengths 3, 4, and 8?

• Yes

• Only if it's an equilateral triangle

• No

• Only if it's a right triangle

Can a triangle be formed if the sum of two sides is equal to the third side?

• Yes, always

• No, never

• No, but there are exceptions

• Yes, but only in special cases

For a triangle with sides 6.2 in, 3 in, and 9 in, how many unique triangles can be formed?

• Two

• Infinite

• One

• None

Which set of side lengths can form a triangle according to the Triangle Inequality Theorem?

• 7 cm, 7.5 cm, 4.5 cm

• 2 cm, 2 cm, 5 cm

• 6 cm, 10 cm, 15 cm

• 5 cm, 5 cm, 15 cm

What is the maximum possible length for the third side of a triangle if the other two sides are 3 in and 8 in?

• 10 in

• 11 in

• 12 in

• 13 in