Perpendicular Bisectors
This line forms a 90-degree angle with a triangle's side and divides it into two equal parts.
What is a perpendicular bisector?
A point on an angle bisector has this relationship to the rays of the angle.
What is equidistant?
This segment connects the midpoints of two sides of a triangle.
What is a midsegment?
In a triangle, the sum of any two sides must have this relationship to the third side.
What is greater than?
This type of proof shows a statement is true by proving its opposite leads to a contradiction.
What is an indirect proof?
The perpendicular bisector of a triangle's side contains all points with this relationship to the endpoints.
What is equidistant?
When the angle bisector of a right angle divides it, each new angle measures this.
What is 45 degrees?
A midsegment is always this fraction of the parallel side of a triangle.
What is one-half?
If one angle in a triangle is larger than another angle, this is true about their opposite sides.
What is the side opposite the larger angle is longer?
A midsegment triangle has this relationship to the original triangle's area.
What is one-fourth?
The equation of a perpendicular bisector must pass through this point of the line segment.
What is the midpoint?
This type of triangle is formed when an angle bisector creates equal angles.
What are congruent triangles?
When all midsegments are drawn in a triangle, this special triangle is formed.
What is a midsegment triangle?
If a, b, and c are sides of a triangle, this inequality must be true.
What is a+b>c?
When proving triangle inequalities, this principle is often used to show one side must be longer than another.
What is the transitive property of inequalities?
In an isosceles triangle, the perpendicular bisector of the base also serves as this.
What is the altitude and median?
The angle bisector of an angle in a triangle divides the opposite side in this ratio.
What is proportional to the lengths of the adjacent sides?
A midsegment of a triangle has this relationship to the third side of the triangle.
What is parallel?
In a triangle, this side is always opposite to the largest angle.
What is the longest side?
When proving two triangles are congruent indirectly, this is often the first step.
What is assume the triangles are not congruent?
The three perpendicular bisectors of a triangle's sides intersect at this point.
What is the circumcenter?
The three angle bisectors of a triangle intersect at this point.
What is the incenter?
When all three midsegments are drawn, they divide the original triangle into this many similar triangles.
What is four similar triangles?
If a, b, and c are sides of a triangle where a>b>c, then their corresponding angles A, B, and C must have this relationship.
What is A>B>C?
In a proof by contradiction involving parallel lines cut by a transversal, this pair of angles is crucial.
What are corresponding angles?