Triangles, Corollaries 1-4, Theorem 3-11/12

Question 1

What is a corollary?

Answer 1

A corollary is a statement that can be proven easily by applying a theorem. Corollaries can be used as reasons in proofs.

Question 2

Corollary #1

Answer 2

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

Question 3

Corollary #2

Answer 3

Each angle of an equiangular triangle has measure 60.

Question 4

Corollary #3

Answer 4

In a triangle, there can be at most one right angle or one obtuse angle.

Question 5

Corollary #4

Answer 5

The acute angles of a right angle are complementary.

Question 6

What is Theorem 3-11?

Answer 6

The sum of the measures of the angles of a triangle is 180.

Contains an axillary line in the diagram

Question 7

What is Theorem 3-12?

Answer 7

The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles,

Question 8

What is the exterior angle of a triangle?

What are the remote interior angles of a triangle?

Answer 8

The exterior of an angle of a triangle is formed when one side of a triangle is extended.

Remote interior angles of a triangle are the other two angles of the triangle.

Question 9

What is the definition of a triangle?

What are the kinds of triangles?

What are the kinds of angles in a triangle?

Answer 9

A triangle is the figure formed by three segments joining three noncollinear points.

The kinds of triangles are; Right, Obtuse, Acute, Equiangular

The kinds of angles in a triangle are; Isosceles, Scalene, Equilateral