| Definitions | Theorems | Theorem Applications | Miscellaneous | More Definitions |
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| 20 | 20 | 20 | 20 | 20 |
| 30 | 30 | 30 | 30 | 30 |
| 40 | 40 | 40 | 40 | 40 |
| 50 | 50 | 50 | 50 | 50 |
| Final Question | ||||
When three or more lines intersect at one point.
When three or more lines intersect at one point.
Concurrent
The point of concurrency for the perpendicular bisectors of a triangle.
The point of concurrency for the perpendicular bisectors of a triangle.
Circumcenter
The point of concurrency for the angle bisectors.
The point of concurrency for the angle bisectors.
Incenter
When all three points of a triangle lie on a circle and the circumcenter of the triangle is the center.
When all three points of a triangle lie on a circle and the circumcenter of the triangle is the center.
Circumscribed Triangle
The use of indirect reasoning, often where only one statement and its negation are the possible outcomes.
The use of indirect reasoning, often where only one statement and its negation are the possible outcomes.
Indirect Proof
Which theorem says that if two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle?
Which theorem says that if two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle?
Hinge
The corollary to the Triangle Exterior Angle theorem says what about the following picture and its angles?
The corollary to the Triangle Exterior Angle theorem says what about the following picture and its angles?
Angle 1's measure is greater than angle two and three.
The triangle inequality theorem says the sum of the lengths of any two sides of a triangle is _____________ than the length of the third side.
The triangle inequality theorem says the sum of the lengths of any two sides of a triangle is _____________ than the length of the third side.
Greater than
If a point is on the perpendicular bisector of a segment, then it is _____________ from the endpoints of the segment.
If a point is on the perpendicular bisector of a segment, then it is _____________ from the endpoints of the segment.
Equidistant
The concurrency of medians theorem states that the point of concurrency is exactly __________ the distance from each vertex to the midpoint of the opposite side.
The concurrency of medians theorem states that the point of concurrency is exactly __________ the distance from each vertex to the midpoint of the opposite side.
Two-Thirds (2/3)
What is always true about the altitudes of a triangle, other than that they make right angles?
What is always true about the altitudes of a triangle, other than that they make right angles?
They are concurrent
If triangle ABC has a bisector that runs from B to D, and D is the midpoint of AC, what does this mean for lengths AB and CB?
If triangle ABC has a bisector that runs from B to D, and D is the midpoint of AC, what does this mean for lengths AB and CB?
They are congruent
If a point is on the bisector of an angle, then the point is ___________ from the sides of the angles.
If a point is on the bisector of an angle, then the point is ___________ from the sides of the angles.
Equidistant
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the _______________.
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the _______________.
Vertices
The bisectors of the angles of a triangle are concurrent at a point equidistant from the ______________ of the triangle.
The bisectors of the angles of a triangle are concurrent at a point equidistant from the ______________ of the triangle.
Sides
True or false: Medians make right angles with the lines they bisect.
True or false: Medians make right angles with the lines they bisect.
False
What is the first step in writing an indirect proof?
What is the first step in writing an indirect proof?
Make a negation assumption
Which of these three statements negate each other: A is parallel to B, A is congruent to B, A is perpendicular to B.
Which of these three statements negate each other: A is parallel to B, A is congruent to B, A is perpendicular to B.
First and Third
Write a negation to the following statement: We did not go to class.
Write a negation to the following statement: We did not go to class.
We did go to class.
What type of triangle will have an orthocenter outside of the triangle?
What type of triangle will have an orthocenter outside of the triangle?
Obtuse
A segment whose endpoints are a vertex and the midpoint of the opposite side.
A segment whose endpoints are a vertex and the midpoint of the opposite side.
Median
The perpendicular segment from a vertex of the triangle to the line containing the opposite side.
The perpendicular segment from a vertex of the triangle to the line containing the opposite side.
Altitude
The point of concurrency of the medians.
The point of concurrency of the medians.
Centroid
The point of concurrency of the altitudes.
The point of concurrency of the altitudes.
Orthocenter
When considering all possibilities and then determining all but one is false, and the remaining answer is true.
When considering all possibilities and then determining all but one is false, and the remaining answer is true.
Indirect Reasoning
What type of triangle will have the orthocenter and centroid in the same position?
What type of triangle will have the orthocenter and centroid in the same position?
Equilateral
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