Centers of Triangles
What is the point where the three medians of a triangle intersect?
The Centroid
Can the side lengths 5 ft, 2 ft, and 10 ft form a triangle? Show your work!
No! 5 + 2 is not > 10
What is the formula for calculating the sum of interior angles of a polygon with n sides?
S = (n - 2)180
What are the properties that define a parallelogram?
1. Opposite sides are parallel.
2. Opposite sides are congruent.
3. Consecutive angles are supplementary.
4. Opposite angles are congruent.
5. Diagonals are bisected.
What properties does a trapezoid have?
1. One pair of parallel lines
2. Consecutive angles are supplementary
Name the point where the angle bisectors of a triangle intersect.
The Incenter
For side lengths 15 m, 50 m, and 37 m, determine if they can form a triangle.
Yes! 15 + 37 > 50
Find the measure of one interior angle of a regular pentagon.
108º
In parallelogram ABCD, if angle A = 60°, what is the measure of angle C?
60º
If a quadrilateral has one pair of parallel sides and the other two sides are congruent, what type of quadrilateral is it?
An isosceles trapezoid
What do you call the point where the perpendicular bisectors of a triangle meet?
The Circumcenter
If two sides of a triangle measure 11 ft and 24 ft, what is the range of possible values for the third side?
13 < x < 35
What is the sum of the exterior angles of a 36-gon?
360º
JKLM is a Rhombus. Find MK.
19.4
Find ∠M.
136º
The circumcenter is equidistant to the ___________ of a triangle.
Vertices/Angles
If two sides of a triangle measure 7 cm and 31 cm, what is the range of possible values for the third side?
24 < x < 38
What is the measure of each exterior angle of a regular octagon?
45º
A(-1,6), B(5,9), C(0,2), D(-8,2)
No!
Find QS.
8.8
Picture. Find BM.
7.6
If QR = 10x - 6, RS = 6x - 15, and QS = x + 24, find the range of possible values for x.
3 < x < 5
If the sum of the interior angles of a polygon is 2340°, how many sides does it have?
15 sides
Use the distance formula to determine what type of quadrilateral WXYZ is.
W(-5, 8), X(-2,14), Y(12,7), Z(9,1)
Rectangle
Find UV.
13