Exploring Triangle Theorems and Addition Postulates

The video tutorial covers key geometry concepts, including the triangle sum theorem, which states that the sum of a triangle's angles is always 180 degrees. It also explains the triangle exterior angle theorem, which relates the exterior angle to the sum of the two remote interior angles. The tutorial provides examples and practice problems to reinforce these concepts. Additionally, it introduces segment and angle addition postulates, which help in calculating lengths and angles. Finally, the transitive property is discussed, highlighting its role in geometric proofs.

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

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

If one angle of a triangle is 68 degrees and another is 33 degrees, what is the measure of the third angle?

• 79 degrees

• 89 degrees

• 99 degrees

• 109 degrees

What does the Triangle Exterior Angle Theorem state?

• The exterior angle is equal to the sum of the two adjacent interior angles.

• The exterior angle is equal to the difference of the two remote interior angles.

• The exterior angle is equal to the sum of the two remote interior angles.

• The exterior angle is equal to the difference of the two adjacent interior angles.

If the exterior angle of a triangle is 93 degrees and one remote interior angle is 28 degrees, what is the measure of the other remote interior angle?

• 55 degrees

• 65 degrees

• 75 degrees

• 85 degrees

Using the Triangle Sum Theorem, if two angles of a triangle are 60 degrees and 70 degrees, what is the measure of the third angle?

• 40 degrees

• 50 degrees

• 60 degrees

• 70 degrees

In a triangle, if one angle is 50 degrees and another is 60 degrees, what is the measure of the exterior angle adjacent to the 50-degree angle?

• 130 degrees

• 120 degrees

• 140 degrees

• 110 degrees

If segment AB is 10 cm and segment BC is 7 cm, what is the length of segment AC?

• 15 cm

• 16 cm

• 17 cm

• 18 cm

If angle AOB is 45 degrees and angle BOC is 15 degrees, what is the measure of angle AOC?

• 65 degrees

• 50 degrees

• 55 degrees

• 60 degrees

What does the transitive property state?

• If a > b and b > c, then a > c

• If a ≠ b and b ≠ c, then a ≠ c

• If a = b and b = c, then a = c

• If a < b and b < c, then a < c

If angle 1 is congruent to angle 3, and angle 1 is also congruent to angle 5, what can be concluded?

• Angle 3 is congruent to angle 4

• Angle 3 is congruent to angle 5

• Angle 4 is congruent to angle 5

• Angle 2 is congruent to angle 5