Midsegment Theorem and Perpendicular Bisectors
Centroid, Circumcenter, Incenter, and Orthocenter
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
Centroid, Circumcenter, Incenter, and/or Orthocenter. Which of these is ALWAYS inside the triangle?
Incenter and Centroid
100
How do you draw a median?
Draw a line from a vertex to the midpoint of the opposite side.
100
TRUE or FALSE: The Converse of the Hinge Theorem states "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."
True
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?
x = 6
200
Which is the center of mass? Centroid, Circumcenter, Incenter, or Orthocenter?
Centroid
200
Angle ABC is split by an angle bisector (line segment BX). Angle ABX has a measure of 34 degrees, what is the value of the angle ABC?
68 degrees.
200
Do the side lengths 6, 6, and 12 work to form a triangle?
no
300
AB = 12
300
TWO PARTS: (a) Which point is the center of a circle that touches all 3 sides of a triangle without overlapping? (b) Which point is the center of a circle that touches all 3 vertices of a triangle?
Centroid, Circumcenter, Incenter, and/or Orthocenter?
(a) incenter
(b) circumcenter
300
Define altitude of a triangle.
the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side
300
In Triangle KLM, the measure of angle K is 40 degrees and the measure of angle L is 55 degrees. List the *sides* from longest to shortest.
KL, KM, LM
400
Toby draws a midsegment in triangle ABC by connecting the midpoints of AB and AC. What side of the triangle is parallel to Toby's midsegment?
BC
400
Where is the circumcenter on a right triangle?
The midpoint of the hypotenuse.
400
The medians of a triangle intersect at a point that is _______ (what fraction?) of the distance from each vertex to the midpoint of the opposite side.
What is two thirds
400
TRUE or FALSE: The hinge theorem states "If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is the side opposite the larger included angle."
True
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
Match the centers to the lines/line segments that meet at that point.
Centers: Centroid, Circumcenter, Incenter, and Orthocenter
Lines/Line Segments: Perpendicular Bisectors, Angle Bisectors, Medians, and Altitudes
Centroid - Medians
Circumcenter - Perpendicular Bisectors
Incenter - Angle Bisectors
Orthocenter - Altitudes
500
(-5, 2)
500
The lengths of two sides of a triangle are 9.8 cm and 14.3 cm. Find the range of the possible lengths of the third side.
4.5 < x < 24.1