6.1
.Find the measure of BAD(CAD=38 degrees)(CAD is half of triangle
38 degrees
what is the circumcenter of a right triangle
on the triangles line
what is the centroid theorem
the centroid of a triangle is two thirds of the distance from each vertex to the midpoint of the opposite side
What is the theorem that states: "the sum of the lengths of any two sides of a triangle is greater than the length of the third side"
Triangle inequality theorem
What is the theorem that states: if two sides of one triangle are congruent to two sides of another triangle, and then the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second."
Hinge Theorem
Find the measures of AB(CA=3.2, AP=3.2, AP is half of AB
6.4
Find the coordinates of the circumcenter of XYZ with vertices X(0,6), Y(0,4), and Z(6,4)
(ans=3,5)
what is the triangle midsegment theorem
the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side
What is an indirect proof
just anything close enough to what a indirect proof is
Is AC or EF longer?
AC
Find the measure of CB(CA=5x+20, CB=8-x)
3.333
Find the coordinates of the circumcenter of ABC with vertices A(2,0), B(6,0), and C(4,4)
Ans=4,1)
In triangle ABC D is the centroid and E is the midpoint of AB, F is the midpoint of AC, and G is the midpoint of BC, AD=6. what is the measure of DG and AG
DG=3 AG=9
What theorem states: "If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side"
Triangle longer side theorem
Is AC or EF longer?
DF
Hypothetical scenario: A hockey goalie stands at the center of the goal, the puck and hitter in line with him, forming two congruent angles on either side. How much distance should the goalie move to block a shot from either the left goalpost or the right, and what theorem proves this?
(Ans=The Angle Bisector theorem, and the goalie will have to move the same distance to block either shot.)
ND=4x-3 and NF=8x-7. What is NE?
Ans=1
the triangle with the vertices A(-2, 5) B(-6, 1)
C(2, -1)) with a midsegment of DE D being the midpoint of AB and E being the midpoint of AC
prove that DE is parallel to BC and that DE = 1/2 of BC
D=(-4,3) E=(0, 2)
because Square root of 17= square root of 2 outside of square root of 17
What are the possible lengths of x
answer 3 < x >17
What is the definition of the hinge theorem?
"What is the definition of the Converse of the Hinge Theorem
Write an equation of the perpendicular bisector of the segment with endpoints X(-3,1) and Y(5,3)
(Ans= -4x-11)
Someone wants to open a shop equidistant from the three streets in the boulevard for the maximum amount of foot traffic. Should the location of their shop be at the circumcenter or the incenter of the triangular boulevard? Explain
the answer is the incenter)
find the orthocenter of a triangle with the vertices X(-5,-1) Y(-2, 4) Z(3, -1)
(-2, 2)
List the angles of triangle ABC in order of smallest to largest while AB=7.2 BC=5.6 AC=6.4
A B C
Is the angle of BAC smaller than the angle of EDF
Yes