Exploring Triangle Exterior Angles and Their Proofs

The video tutorial explains a theorem about the relationship between an exterior angle of a triangle and the sum of its interior opposite angles. It begins with a review of key concepts such as straight angles and the sum of angles in a triangle. The tutorial then defines exterior and interior opposite angles, illustrating the six possible exterior angles in a triangle. The main focus is on proving that the exterior angle is equal to the sum of the two interior opposite angles, using a step-by-step approach without additional construction. The proof is based on the properties of angles and equations, ensuring a clear understanding of the theorem.

What is the measure of a straight angle?

• 360°

• 180°

• 45°

• 90°

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

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

• 180°

• 270°

• 90°

• 360°

Tags

CCSS.8.G.A.5

What is an exterior angle of a triangle?

• An angle inside the triangle

• An angle formed by extending one side of the triangle

• An angle equal to 90°

• An angle equal to 45°

Which angles are considered the interior opposite angles?

• Angles equal to 90°

• Angles adjacent to the exterior angle

• Angles inside the triangle opposite to the exterior angle

• Angles outside the triangle

Tags

CCSS.8.G.A.5

How many possible exterior angles does a triangle have?

• Three

• Four

• Five

• Six

Tags

CCSS.8.G.A.5

What is the first step in setting up the proof of the theorem?

• Labeling the angles

• Drawing a triangle and extending one side

• Calculating the angles

• Writing down the given information

Which angle is labeled as the exterior angle in the proof?

• Angle 4

• Angle 3

• Angle 2

• Angle 1

Tags

CCSS.8.G.A.5

What is the goal of the proof?

• To show that the exterior angle is equal to the sum of the interior opposite angles

• To find the measure of angle 3

• To prove that the sum of the angles in a triangle is 180°

• To calculate the measure of angle 4

Tags

CCSS.8.G.A.5

What is the measure of angles 3 and 4 combined?

• 90°

• 180°

• 270°

• 360°

Tags

CCSS.4.MD.C.7

What is the final step in proving the theorem?

• Multiplying the angles

• Adding angles 1 and 2

• Dividing the angles

• Subtracting angle 3 from both sides of the equation

Tags

CCSS.HSG.CO.C.9