Midsegment Theorem and Coordinate Proofs
Perpendicular Bisectors
Angle Bisectors
Medians and Altitudes
Inequalities One and Two Triangles
100
What does the midsegment of a triangle do?
What is 'connects the midpoints of two sides of a the triangle'.
100
What is a point equidistant from the endpoints of a segement?
What is a perpendicular bisector.
100
What does the angle bisector theorem state?
What is, if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
100
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.
100
What is the Converse of the Hinge Theorem?
What is, if two sides of one triangle are congruent to 2 sides of another triangle, and the third side of the first triangle is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
200
Midsegment length: 8x-25
Base length: 13x-150
Find x.
Find x.
What is 25.
200
The two lines that run from the perpendicular bisector to the base on opposing sides are valued at 3x+9 and 5x-3. What is the value of x?
What is 6.
200
If two angles are seperated by the angle bisector and one of the is 34 degrees, what is the value of the entire angle?
What is 68 degrees.
200
Define altitude of a triangle.
What is the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.
200
Do the side lengths 6+72/2, 6*8, and 12*12/4 work to form a triangle?
What is yes.
300
What point should almost any coordinate proof have?
What is (0,0).
300
What are the three things that can make a point of concurrency?
What is lines, rays, and segments.
300
What is the point of concurrency of the three angle bisectors of a triangle?
What is the incenter.
300
Where is the orthocenter of an obtuse triangle?
What is outside the triangle.
300
Given: the boy is 4'8" tall.
Prove: his name is Tanaka.
What temporary assumption would one make to start an indirect proof?
What temporary assumption would one make to start an indirect proof?
What is, his name is not Tanaka.
400
If a square has the area of xy, name four coordinates that could be used.
What is (0,0), (0,x), (y,0), and (y,x).
400
The perpendicular bisectors of a triangle all pass through what point?
What is the circumcenter
400
If a triangle is made using an angle bisector, a perpendicular bisector, and a base, and the angle bisector's length is 15 and the base's length is 9, what is the perpendicular bisector's length?
What is (roughly) 17 and a half.
400
In what type of triangle can one of the points be one of the points of concurrency of a triangle?
What is a right triangle.
400
AB=AE. AF is equal to itself. BF is 22 units and EF is 13*6/5+6.
What angle is bigger, BAF or EAF?
What angle is bigger, BAF or EAF?
What is BAF.
500
If the midsegment of a triangle is 3x+3 and its opposite side is 4x+7, what is the value of x?
What is x=1/2?
500
What is AB = 12
500
What is x = 5
500
What is (-5, 2)
500
True or False:
The Triangle Inequality Theorem states that the length of any side of a triangle must be greater than the sum of the lengths of the other two sides.
The Triangle Inequality Theorem states that the length of any side of a triangle must be greater than the sum of the lengths of the other two sides.
What is false