Polygons
If you add up all the exterior angles in a polygon, what do they equal?
360 degrees
In a tessellation, the sum of the angles at any vertex is how many degrees?
360 degrees
A quadrilateral with two pairs of parallel sides.
Rectangles, Rhombuses, and squares have the properties of what?
Parallelograms
Explain why a trapezoid is not a parallelogram
Trapezoids only have one pair of parallel sides, parallelograms have two.
What is the equation to find the sum of the interior angles of any polygon?
sum = (n - 2)180
How many squares do you need to make a tessellation?
Four
List the properties that relate to the angles of a parallelogram.
opposite angles are congruent and consecutive angles are supplementary
A square has the properties of these two quadrilaterals.
Rectangle and a Rhombus
What is the equation used to find the length of a midsegment in a trapezoid?
midsegment = (base 1 + base 2) /2
What is the equation to find the measure of one interior angle of a regular polygon?
1 int. angle = (n - 2) 180 divided by n
How many triangles do you need to form a tessellation?
Six
List the properties that relate to the sides and the diagonals of parallelograms.
Opposite sides are parallel, Opposite sides are congruent, and the diagonals bisect each other.
if you draw one diagonal in a square. What type of triangle do you create?
a 45 - 45 - 90 special right triangle
What three things are congruent in an isosceles trapezoid?
the base angles, the legs, and the diagonals
If you have a regular polygon, what is the equation to find the measure of one exterior angle?
ext angle = 360 / n
Will these tessellate? and how many?
hexagon, triangle, square
Yes, 1 hexagon, 1 triangle, and 2 squares
consecutive angles are supplementary
What are two properties that are specific to a rectangle?
a rectangle has four right angles and two congruent diagonals.
Kites and rhombuses share this property
the diagonals are perpendicular
What is the name of a polygon where the sum of the interior angles is 1,260?
n = 9, nonagon
You have a tessellation that has 3 regular polygons, one is a square, one is a hexagon. How many sides does the 3rd polygon have?
n = 12
Finish this conditional statement: if you can show that one pair of opposite sides .............then it is a parallelogram
are both parallel and congruent
What two properties are specific to a rhombus (and square)?
The diagonals are perpendicular and the diagonals bisect the opposite angles.
Draw a diagram of a kite with two diagonals, label the vertices KITE. Label everything! Which two angles (KITE) are the two congruent angles?
the pair of opposite angles that are in between the sides of two different lengths.