Special Segments and Concurrency Flashcards
Deine the Median
A segment that joins a vertex of a triangle with the midpint of the opposite side. (midpoint to the endpoint.)
Define the Centroid
The intersection of the three medians of a triangle. Located 2/3 of the distance from the vertex to the midpoint.
What is the altitude
A segment from a vertex of the triangle perpendicular to a line containing the opposite side. May be outside the triangle. Remember: Creates a triangle, and is the height).
In terms of altitude, describe an obtuse triangle:
It has 2 points outside the triangle.
What is the orthocenter
The intersection of the three altitude of a triangle
Define Angle Bisector
A segment that bisects the vertex angle of a triangle. Divide the angle in half
Incenter Definition
The intersection of the three angle bisectors. The incenter is the center of an inscribed circle in the triangle.
Define Perpendicular Bisector
A segment that passes through the midpoint of a side and is perpendicular to that side.
Define Circumcenter
The intersection of the three perpendicular bisector of a triangle. The circumcenter is the center of a circle that cirumscribes the triangle.
What is the rule of the Vertex Angle?
It is not congruent with other angles.
What is the point of concurrency for an angle bisector?
Incenter
What is the point of concurrency for the Medians of a triangle?
Centroid
What is the point of concurrency for the altitudes of a triangle?
Orthocenter
What is the point of concurrency for the Perpendicular bisectors of a triangle?
Circumcenter
How do you order the angles of a triangle given the side lengths?
If one side of the triangle is larger than the other, then the angle opposite is greater.
How do you order the sides of a triangle given the angles?
If one angle is larger than another, the opposite side of the greater angle is larger.
What is the rule for determining if three numbers can form a triangle?
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. If this is true, then the measures will form a triangle.
Do Perpendicular Bisectors have to connect to both sides of a triangle?
No, only one
What is a midsegment?
Connects the midpoints of two sides of a triangle
The incenter is equidistant from each ________ of a triangle.
Vertex
The circumcenter is equidistant from the __________ of a triangle.
Perpendicular Bisector
The Centroid is _______ of the distance from each vertex to the midpoint of the opposite side.
2/3
When asked to find the median of given coordinates, what is the rule?
Take the other two coordinates, add x’s and y’s up and divide each by two. These new coordinates are the answers.
What is the Pythagorean theorum?
Square root of (X2-X1)Squared + (Y2-Y1) Squared
How do you find the length of coordinate sides of a triangle?
Use the Pithagoreum theorem
What is the exterior Angle theorem?
States that the measure of a triangle’s exterior angle is greater than either interior angles.
