Vocabulary
Two or more points that are the same distance from a particular point.
What is equidistant?
The common point of the altitudes.
What is the orthocenter?
Line AD is a perpendicular bisector of line BC. Is triangle ABC acute or obtuse?
Acute
The property that is the reason for a proof statement that says EF is congruent to EF.
Reflexive property
These are the four ways to prove right triangle congruence.
HL, LL, LA, HA
A segment that bisects one of the angles of a triangle.
What is the angle bisector?
The common point of the medians.
What is the centroid?
Point D is the centroid of triangle ABC. Median line AE intersects line BC, median line BF intersects line AC, and median line CG intersects line AB. If AE=30, BD=6, and DG=12. What is the length of BF?
18
These are the four ways to prove triangle congruence.
AAA, SSS, SAS, AAS
The segment from a vertex that is perpendicular to the base or to the line containing to the opposite side.
What is the altitude?
The common point of the angle bisectors.
What is the incenter?
Triangle ABC has angle measures where A = 60, B = 30, and C = 90. List the line segment of the triangle from least to greatest.
AC, BC, AB
If a point at the center of a triangle is equidistant to all three sides, then that point is the incenter.
What is the converse of the incenter theorem?
If two sides of a triangle are congruent, then the angles opposite of those sides are also congruent.
What is the triangle congruence theorem?
A line that is perpendicular to the base and splits the base into two congruent parts.
What is perpendicular bisector?
The common point of the perpendicular bisectors.
What is the circumcenter?
Triangle EFG has a median line ED that intersects line GF. GD = 3x + 2 and DF = 5x -2. Solve for the length of GF.
16
The sum of any two length of a triangle must be greater than the third length.
What is the triangle inequality theorem
If a triangle is equiangular (all angles are equal), then it is also equilateral (all sides are equal).
What is the converse of equilateral triangle theorem?
The common points for these are called centroids. The centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.
What are the medians?
The point where three or more lines intersect.
What is the point of concurreny?
The vertices of a triangle ABC are A(0,0), B(5,0) and C(1,4). Find the orthocenter.
(1, 8/5)
If two triangles have two congruent sides, then the triangle with the longer included angle has a longer side opposite the angle.
Hinge theorem
What rule would you use to prove that triangle EFG and triangle ABC are congruent given that EF is congruent to AB, FG is congruent to BC, and angle F is congruent to angle B.
SAS