Exploring Triangle Angle Relationships

The video tutorial covers the fundamental properties of triangles, focusing on the sum of angles in a triangle, which is always 180 degrees. It provides a formal proof using parallel lines and alternate interior angles. The tutorial also explores the properties of isosceles triangles, emphasizing congruent sides and base angles. Finally, it introduces the external angle theorem, demonstrating how an external angle equals the sum of the two remote interior angles.

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

• 90 degrees

• 270 degrees

• 180 degrees

• 360 degrees

If you place the three angles of a triangle side by side, what do they form?

• A square

• A circle

• A straight line

• A right angle

In the formal proof, what is added to the triangle to help prove the angle sum property?

• A median

• A perpendicular line

• A parallel line

• A bisector

Which angles are equal due to the alternate interior angle theorem in the formal proof?

• Angles 1 and 2

• Angles 2 and 3

• Angles 5 and 2

• Angles 4 and 1

If a triangle has angles of 112 degrees and 24 degrees, what is the measure of the third angle?

• 52 degrees

• 36 degrees

• 24 degrees

• 44 degrees

In an isosceles triangle, what are the equal sides called?

• Bases

• Legs

• Vertices

• Hypotenuses

What is the measure of each base angle in an isosceles triangle if the vertex angle is 36 degrees?

• 72 degrees

• 36 degrees

• 108 degrees

• 54 degrees

What is an external angle in a triangle?

• An angle inside the triangle

• An angle formed by extending one side of the triangle

• An angle formed by the intersection of medians

• An angle formed by the intersection of altitudes

What do the remote interior angles of a triangle add up to in relation to the external angle?

• They are double the external angle

• They are unrelated to the external angle

• They are equal to the external angle

• They are half of the external angle

If an external angle of a triangle is 160 degrees and one remote interior angle is 42 degrees, what is the measure of the other remote interior angle?

• 138 degrees

• 20 degrees

• 42 degrees

• 118 degrees