Triangle Properties and Theorems

The video tutorial explores the concept of unique triangles, focusing on how given measurements can result in one unique triangle or multiple possibilities. It covers the basics of triangles, including the triangle inequality theorem, and discusses conditions under which a triangle is unique. The tutorial also examines scenarios where multiple triangles can be constructed and outlines criteria for ensuring a unique triangle. The essential question is how to determine if given measurements will produce one unique triangle.

What is the essential question addressed in the video?

• How to calculate the area of a triangle?

• How to determine if given measurements produce one unique triangle?

• How to classify triangles based on angles?

• How to find the perimeter of a triangle?

Which theorem states that the sum of any two sides of a triangle must be greater than the third side?

• Pythagorean Theorem

• Triangle Inequality Theorem

• Congruence Theorem

• Angle Sum Theorem

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

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

If a triangle has angles of 30 and 90 degrees, what is the measure of the third angle?

• 120 degrees

• 90 degrees

• 60 degrees

• 45 degrees

Why can't a triangle have angles of 90 and 100 degrees?

• Because it would be an equilateral triangle

• Because it would be an obtuse triangle

• Because the sum exceeds 180 degrees

• Because it would be a right triangle

What is the result when you add the two smaller sides of a triangle?

• It is less than the third side

• It is greater than the third side

• It equals the third side

• It forms a right angle

If given three side lengths, how many unique triangles can be formed?

• None

• Infinite

• One

• Two

What happens if you flip or rotate a triangle with given side lengths?

• It remains the same triangle

• It becomes a different triangle

• It changes its area

• It changes its perimeter

When given two sides and an angle, under what condition is only one unique triangle formed?

• When the angle is opposite the longer side

• When the angle is between the two sides

• When the angle is a right angle

• When the angle is an obtuse angle

How many unique triangles can be formed with two sides and an angle not between them?

• None

• Multiple

• Two

• One