Perpendicular Bisectors
What is the point of concurrency for perpendicular bisectors called?
Circumcenter
What is the point of concurrency for angle bisectors called?
Incenter
What is the point of concurrency for medians called?
Centroid
What is the point of concurrency for altitudes called?
Orthocenter
Fill in the blanks: The longest side of a triangle is opposite the ______________ angle and the smallest angle in a triangle is opposite the _______________ side.
Biggest or Largest, Shortest or Smallest
Describe what the perpendicular bisector of a triangle looks like.
It cuts the side in half and intersects the side at a right angle.
Describe what the angle bisector of a triangle looks like.
A ray that cuts an angle in half.
Describe what the median of a triangle looks like.
Starts at the vertex and cuts the opposite side in half (or connects to the opposite side's midpoint).
Describe what the altitude of a triangle looks like.
Starts at a vertex and meets the opposite side at a right angle.
If two sides of a triangle are 6 in. and 18 in., what are the possible lengths of the third side length?
12 in. < x < 24 in.
or
24 in. > x > 12 in.
What is important for us to know about the circumcenter of a triangle?
It is equidistant from the vertices.
What is important for us to know about the incenter of a triangle?
It is equidistant to the sides.
What is important for us to know about the centroid of a triangle?
It cuts the median into two pieces, the longer is 2/3rds of the total length and the shorter is 1/3rd of the total length.
In which type of triangle is it easiest to find the orthocenter?
Right Triangle.
In triangle ABC, if A=30 degrees, B=50 degrees and C=100 degrees, list the side lengths from LONGEST to SHORTEST.
AB, AC, BC
If the radius of the circumscribed circle is 14 in, what is the distance from the circumcenter to a vertex of the triangle.
14 in.
If the radius of the inscribed circle is 8 in, what is the distance from the incenter one side of the triangle?
8 in.
The length of median AC=18. A is the vertex of the triangle and C is the midpoint of the opposite side. Point B is the centroid of the triangle. What is the length of AB?
12
A triangle has the coordinates (2,1), (-4,1) and (-4,8). What are the coordinates of the orthocenter?
(-4,1)
Can side lengths of 12, 13, and 26 create a triangle?
No, 12+13=25 which is less than 26
In triangle XYZ, point C is the circumcenter and point B is the midpoint of side XY. If CB=5 and XY=24, what is the length of CY?
CY=13
The distances from the incenter to two different sides of a triangle are labeled by the expressions 2x+7 and 3x-4. What is the radius of the inscribed circle?
r=29
In triangle TUV, Median TR=24. The centroid is labeled by point Z. If the length of TZ=2x-4, what is x?
x=10
Triangle ABC is an isosceles triangle with AB as the base. The AC=24, BC=24 and AB=30. The altitude starting at vertex C is drawn and intersects with side AB at point D. What is the length of AD?
AD=15