Points of Concurrency
Perpendicular Bisectors
Angle Bisectors
Medians
Inequalities One and Two Triangles
100
What is the point of concurrency for perpendicular bisector?
circumcenter
100
A point equidistant from the endpoints of a segment is on the ________ of the segment.
perpendicular bisector.
100
If a point is on the bisector of an angle, then it is equidistant from _____________.
the 2 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.
2/3rds
100
The Converse of the Hinge Theorem allows you to compare the size of 2 ________ in different triangles
angles
200
What is the point of concurrency for angle bisectors?
incenter
200
If one of the two lines that run from the perpendicular bisector to the base on opposing sides is valued at 13 and the other is 4x-3. What is the value of x?
x = 4
200
If two angles are separated by the angle bisector and one of the angles is 34 degrees, what is the value of the entire angle?
68 degrees.
200
True or False. In an equilateral triangle, median, perpendicular bisector, and angle bisector are all the same line, segment, or ray.
True
200
Do the side lengths 6 cm, 8 cm, and 12 cm work to form a triangle? Explain how you know.
yes. 6 + 8 > 12
300
What is the point of concurrency for medians of a triangle?
centroid
300
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?
x=6
300
What is the point of concurrency of the three angle bisectors of a triangle?
the incenter.
300
The medians of a triangle intersect at a point that is _______ of the distance from each centroid to the midpoint.
1/3
300
Is it possible to have sides of a triangle with lengths 13, 5, 19?
No
400
The circumcenter is equidistant from the __________ of the triangle.
vertices
400
The perpendicular bisectors of a triangle all meet at what point of concurrency?
the circumcenter
400
The incenter which is the point of concurrency for angle bisectors is equidistant from each _________.
side
400
The median of a triangle has a length of 12. What is the distance from the vertex to the centroid?
8
400
AB = 4 cm, BC = 5 cm, and AC = 7 cm.
What is the largest angle in triangle ABC?
angle B.
500
What are the three things that can make a point of concurrency?
What is lines, rays, and segments.
500
AB = 12
500
Solve for x.
x = 5
500
What is the circumcenter of a triangle with these vertices:
A(0,6), B(4,0), C(0,0)
(2,3)
500
Angle A = 67 degrees. Angle B = 75 degrees. What is the smallest side of triangle ABC?
AB.