Proving the Triangle Angle Sum Theorem

The video tutorial explains the proof that the sum of angles in a triangle is 180 degrees. It begins with constructing a line parallel to one side of the triangle and naming the angles formed. The concept of alternate interior angles is introduced, showing that certain angles are equal. By substituting these angles, it is demonstrated that the sum of the interior angles of the triangle equals 180 degrees, using the property of a straight line.

What is the sum of the angles within a triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

Tags

CCSS.8.G.A.5

Which line is drawn parallel to BC in the construction?

• AD

• EF

• GH

• IJ

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

How many interior angles are there in triangle ABC?

• 1

• 4

• 2

• 3

Tags

CCSS.8.G.A.5

What are the names of the angles formed outside the triangle?

• Angle 4 and Angle 5

• Angle 2 and Angle 3

• Angle 1 and Angle 2

• Angle 5 and Angle 6

What is the relationship between angle 2 and angle 4?

• They are complementary angles

• They are supplementary angles

• They are alternate interior angles

• They are corresponding angles

Tags

CCSS.8.G.A.5

What must a transversal cut to form alternate interior angles?

• Two intersecting lines

• Two perpendicular lines

• Two skew lines

• Two parallel lines

Tags

CCSS.8.G.A.5

Which angles are equal due to being alternate interior angles in the original figure?

• Angle 2 and Angle 4

• Angle 1 and Angle 4

• Angle 1 and Angle 5

• Angle 3 and Angle 4

Tags

CCSS.8.G.A.5

Which line acts as the transversal intersecting the parallel lines BC and EF?

• AB

• AC

• AD

• AE

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

What is the sum of angles 1, 4, and 5?

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

Tags

CCSS.7.G.B.5

What does the sum of angles 1, 2, and 3 equal?

• 180 degrees

• 90 degrees

• 360 degrees

• 270 degrees

Tags

CCSS.4.MD.C.7