Perpendiculars & Bisectors
Bisectors of a Triangle
Medians & Altitudes
Midsegment Theorem
100
A segment, ray, line, or plane that is perpendicular to a segment at its midpoint
What is a perpendicular bisector
100
A line (or ray or segment) that is perpendicular to a side of the triangle at the midpoint of the side.
What is a perpendicular bisector of a triangle
100
A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.
What is a median of a triangle
100
The segment that connects the midpoints to the two sides of a triangle.
What is a midsegment of a triangle
200
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
What is Perpendicular Bisector Theorem
200
When three or more lines (or rays or segments) intersect in the same point
What are concurrent lines
200
The centroid of a triangle is the point where three ____ intersect
What is a median
200
The segment connecting the midpoints of two sides of a triangle is ____ to the third side and is ____ as long.
What is parallel; half
300
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
What is Angle Bisector Theorem
300
The point of concurrency of the perpendicular bisectors of a triangle, which is equidistant from the three vertices of a triangle
What is the circumcenter of the triangle
300
The medians of a triangle intersect at a point that is ____ of the distance from each vertex to the midpoint of the opposite side.
What is two-thirds
300
Suppose you were given only the three midpoints of the sides of a triangle. Is it possible to draw the original triangle?
What is yes, plot coordinates in a plane and calculate slopes then draw sides using midpoints.
400
If D is on the ____ of segment AB, then it is equidistant from A to B.
What is a perpendicular bisector
400
The point of concurrency on an: acute triangle, right triangle, and obtuse triangle
What is inside, on, and outside the triangle
400
This point is always located on the inside of a triangle
What is centroid
400
Method for verifying that the midsegment theorem is true for a given midsegment, given its vertices.
What is using slope and distance formula.
500
Point G is in the interior of
Point G is on the bisector of <HJK
500
The point of concurrency of the angle bisectors of a triangle
What is the incenter of the triangle
500
Where the orthocenter is located on an acute, right, and obtuse triangle.
What is inside, on, and outside.
500
Use a straight edge to draw a triangle. Then use the straight edge and compass to construct the three midsegments of the triangle.
see sketch
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