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Theorems/Definitions
Find the Measure
This & That
Misc.
Final
100

The angles in a triangle add up to ________.

180 degrees

100

Find the unknown angle measure (Figure 1)

83 degrees

100

A perpendicular bisector is a segment that is perpendicular AND bisects a side of a triangle. What is the point of concurrency called where the three perpendicular bisectors meet?

circumcenter of a triangle

100

The point of concurrency of the angle bisectors is called the __________.

Incenter 

200

According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle equal the _______ of its remote interior angles.

Sum

200

Find the unknown angle measure (Figure 2)

32 degrees

200

The circumcenter of Triangle ABC is point P. Find the length of side PC. (Figure 4)

PC = 71 units

200

An _______________ is a perpendicular segment from a vertex in a triangle to the opposite side or to a line that contains the opposite side. 

Altitude

300

According to the Isosceles Triangle Theorem, if two sides of a triangle are congruent, then the two angles ____________ the congruent sides are congruent.

opposite

300

Find the unknown angle measure (Figure 3)

73 degrees

300

What are the steps to solving for the circumcenter of a triangle. (7 Steps)

1. Find the midpoint of one side

2. Find that slope of that side

3. Find the equations of the lines that is perpendicular to the line you used 

4. Repeat steps 1-3 with another side

5. Set the two equations equal and solve for x.

6. Plug x into one of the equations & solve for y.

7. Write the answer as an ordered pair (x, y)

300

The point of concurrency of the altitudes in a triangle is called the _________________. 

Orthocenter

300

1. Find the circumcenter given the points A(1, 4),    B(1, 2) and C(6, 2)

2. Find the orthocenter given the points A(2,6), 

B(8, 6), and C(6,2)

(3.5, 3)

(6, 4)


400
An angle bisector of a triangle divides an angle into two _________ parts

congruent 

400

Find the measure of the following (Figure 5)

AE

Angle DFC

FE

CB

AE = 30 units

Angle DFC = 64 degrees

FE =28.5 units

CB = 45 units

400
A median is a segment whose endpoints are a vertex and the ____________ of the opposite side. 

Midpoint

400

In an acute triangle, the orthocenter is _______ the triangle. 

In an obtuse triangle, the orthocenter is _______ the triangle. 

In a right triangle, the orthocenter is _______ the triangle.

inside

outside

on

500

According to the Centroid Theorem, the centroid of a triangle is located ________ of the distance from each vertex to the midpoint of the opposite side. 

2/3

500

Solve for the variable (Figure 6)

v=5

500

A ________________ is the point of concurrency of the medians in a triangle

centroid

500

A midsegment of a triangle is a segment that joins the ____________ of two sides of a triangle. Midsegments are _______________ to the 3rd side of a triangle and ________ the distance of the length of that parallel side (Triangle Midsegment Theorem).

Midpoints

Parallel

half