Theorems/Definitions
The angles in a triangle add up to ________.
180 degrees
Find the unknown angle measure (Figure 1)
83 degrees
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
The point of concurrency of the angle bisectors is called the __________.
Incenter
According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle equal the _______ of its remote interior angles.
Sum
Find the unknown angle measure (Figure 2)
32 degrees
The circumcenter of Triangle ABC is point P. Find the length of side PC. (Figure 4)
PC = 71 units
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
According to the Isosceles Triangle Theorem, if two sides of a triangle are congruent, then the two angles ____________ the congruent sides are congruent.
opposite
Find the unknown angle measure (Figure 3)
73 degrees
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)
The point of concurrency of the altitudes in a triangle is called the _________________.
Orthocenter
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)
congruent
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
Midpoint
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
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
Solve for the variable (Figure 6)
v=5
A ________________ is the point of concurrency of the medians in a triangle
centroid
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