Midsegment Theorem
Perpendicular Bisectors
Angle Bisectors
Medians and Altitudes
Inequalities in Triangles
100
What does the midsegment of a triangle connect?
the midpoints of two sides of a triangle
100
Always, Sometimes, or Never.
Perpendicular bisectors ___________ pass through a vertex.
sometimes
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 relationship between the slope of a midsegment and the slope of the opposite side?
They are the same. The midsegment and the opposite side are parallel.
200
Any point on the perpendicular bisector of a segment is the same distance from the __________ of the segment.
endpoints
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
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.
Yes. 6 + 8 > 12.
300
How many midsegments does a triangle have?
3
300
Find the distance between (1,2) and (5,5)
5
300
Always, Sometimes, or Never.
Angle bisectors ___________ have a vertex as one endpoint and always intersect inside the triangle.
always
300
The orthocenter is the intersection of the ________ of a triangle.
altitudes
300
In triangle ABC and triangle DEF, AB is congruent to DE, BC is congruent to EF, and AC < DF. So m<____ is greater than m>_____ by the converse of the hinge theorem.
m<E is greater than m<B
400
Midsegment length: 6x-25
Opposite side length: 13x-150
Find x.
x = 100
400
The perpendicular bisectors of a triangle all pass through what point of concurrency?
the circumcenter
400
The intersection of the angle bisectors of a triangle is the __________.
incenter
400
In what type of triangle is the circumcenter on one of the sides?
a right triangle.
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 length of the midsegment?
4.5
500
A(0,1), B(4,3).
Write the equation of the perpendicular bisector of AB.
Answer is slope-intercept form.
y = -2x + 6
500
Solve for x if CB and DB are congruent
x = 3
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.