Show:
Midsegment Theorem
Perpendicular Bisectors
Angle Bisectors
Medians and Altitudes
Inequalities One and Two Triangles
100
What does the midsegment of a triangle connect?
the midpoints of two sides of a the triangle.
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 centroid is the center of __________ of a triangle.

Mass

100
The Converse of the Hinge Theorem allows you to compare the size of 2 ________ in different triangles
angles
200
What is the relationship between the slope of a midsegment and the slope of the opposite side?
They are the same.
200
The perpendicular bisectors of a triangle all meet at what point of concurrency?
the circumcenter
200
What is the point of concurrency of the three angle bisectors of a triangle?
the incenter.
200
Define or describe the altitude of a triangle.
What is the perpendicular segment from a vertex to the opposite side.
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
How many midsegments does a triangle have?
3
300

The circumcenter of a triangle is equidistant from the ___________ of the triangle.

Vertices

300
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.
300
The orthocenter is the intersection of the ________ of a triangle.
altitudes
300
Define the inverse of a conditional statement.
Negate both the hypothesis and conclusion.
400
Midsegment length: 8x-25 Opposite side length: 13x-150 Find x.
x = 25
400

The CONVERSE to the perpendicular bisector theorem is used to prove that.....

A point is on the perpendicular bisector

400

The incenter is equidistant from the ______________ of a triangle

Sides

400
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
400
AB = 4 cm, BC = 5 cm, and AC = 7 cm. What is the largest angle in triangle ABC?
angle B.
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
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
500

In triangle ABC, the distance from the circumcenter to angle A is 2x+1. The distance from the circumcenter to angle B is 4x-9. Find x

x = 5

500
In what type of triangle is the circumcenter on one of the sides?
a right triangle.
500
Angle A = 67 degrees. Angle B = 75 degrees. What is the smallest side of triangle ABC?
AB.