Lines in a Triangle
Points of Concurrency
Triangle Inequalities
Midsegments and Medians
Perpendicular and Angle Bisectors.
100
The segment that connects the midpoints of two sides of the triangle.
What is the midsegment?
100
The point at which three or more lines, rays, or segments intersect.
What is the point of concurrency?
100
List the sides from least to greatest.
SR, QS, and QR.
100
In triangle ABC, x is the centroid. If DC = 24, find DX.
DX = 8
100
Find the value of x and the length of MN.
x = 14
MN = 85
200
A segment, ray, line, of plane that is perpendicular to a segment at its midpoint.
What is a perpendicular bisector?
200
The point of concurrency where the three medians of a triangle meets. This point is two-thirds of the distance to the vertex to the midpoint of the opposite side.
What is a centroid?
200
The lengths of two sides of a triangle are given. Determine the range of value of the possible lengths of the third side.
8, 15
7 < x < 23
200
Find the value of x.
x = 16
200
Find the coordinates of the circumcenter of the triangle below. Give the answer as an ordered pair.
(8, 6)
300
A ray, segment, or line that divides an angle into two angles that are congruent.
What is an angle bisector?
300
The point at which the lines containing three altitudes of a triangle intersect.
What is the orthocenter?
300
Tell which theorem could be used to prove <D > <R.
Converse of the Hinge Theorem.
300
Find the value of x.
x = 5
300
If Q is the incenter of triangle MNP, find KQ, JQ, and the measure of angle QNL.
KQ = 5
JQ = 5
m<QNL = 18
400
A segment from a vertex to the midpoint of the opposite side.
What is a median?
400
The point of concurrency of the three angle bisectors of a triangle. This point is equidistant from the sides of a triangle.
What is an incenter?
400
Find the range of possible values for each variable.
4 < x < 26
400
In triangle ABC, x is the centroid. If AX = 11, find XE.
XE = 5.5
400
If D is the incenter of triangle ABC, find x, and the measure of PD and MD.
x = 12
PD = 20
MD = 20
500
The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.
What is an altitude.
500
The point of concurrency of the three perpendicular bisectors of a triangle that is equidistant from the vertices of the triangle.
What is a circumcenter?
500
Find the range of possible values for each variable.
5/2 < x < 30
500
Find the value of each variable.
x = 15
y = 7
z = 13
500
Find the value of x and y. Then find the measure of BC and angle AFB.
x = 6
y = 10
BC = 58
<AFB = 40 degrees