L4.6 Application of Triangle Theorems

L4.6 Application of Triangle Theorems

Geometry

Triangle Theorems

• The sum of the measures of the interior angles of a triangle is 180∘.

• The base angles of an isosceles triangle are congruent.

• If a triangle has two congruent angles then it is isosceles.

• The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

• The segment connecting two midpoints of a triangle is both parallel to and one half the length of the third side of the triangle.

Triangle Theorems

• The three medians of a triangle meet at a point called the centroid. The centroid divides each median in a 2:1 ratio with the larger segment being the one from the vertex to the centroid.

• The three angle bisectors of a triangle meet at a point called the incenter.

• The three altitudes of a triangle meet at a point called the orthocenter.

• The three perpendicular bisectors of a triangle meet at a point called the circumcenter.

Fill in the Blanks

Fill in the Blanks

Prove that two of the medians of an isosceles triangle are congruent

• Hint: prove that ΔDBC≅ΔECB and then show that the medians are congruent because they are corresponding parts of the triangles.

Fill in the Blanks

Fill in the Blanks

Open Ended

Name the four points of concurrency for a triangle.

Multiple Choice

Which of these is called the center of gravity.

• orthocenter

• incenter

• circumcenter

• centroid

Multiple Choice

What is the point of concurrency?

• Orthocenter

• Circumcenter

• Incenter

• Centroid

Multiple Choice

What type of special segments are being used?

• Perpendicular Bisectors

• Angle Bisectors

• Medians

• Altitudes

Multiple Choice

What type of special segments are being used?

• Altitudes

• Perpendicular Bisectors

• Medians

• Angle Bisectors

Multiple Choice

What is the point of concurrency?

• Orthocenter

• Centroid

• Circumcenter

• Incenter

Multiple Choice

If D is the orthocenter, what type of segments are drawn?

• medians

• altitudes

• angle bisectors

• perpendicular bisectors

Multiple Choice

Name the point of concurrency shown.

• Circumcenter
• Incenter
• Supercenter
• Neither

Multiple Choice

The figure is an example of a(n) ...

• altitude

• perpendicular bisector

• midsegment

• angle bisector

Multiple Choice

The figure is an example of a(n) ...

• angle bisector

• midsegment

• altitude

• median