ANGLES & POLYGONS
In a parallelogram, opposite angles are ______
congruent
Name 3 types of special parallelograms
Rhombus, Rectangle, & Square
What makes a parallelogram a rectangle?
4 right angles
What is the difference between a rhombus and a square?
A rhombus only has to have 4 congruent sides, and a squares must also have 4 right angles
What makes an isosceles trapezoid different than a regular trapezoid? State two things.
congruent legs
base angles are congruent
diagonals are congruent
What is the angle sum of any quadrilateral?
360 degrees
Consecutive angles in a parallelogram are __________
supplementary
What is true about the diagonals of a rectangle
the diagonals are congruent
the diagonals bisect each other
Always, sometimes, or never? A rhombus is ________ a square.
sometimes
What is the midsegment formula for a trapezoid?
midsegment = 1/2(b1 + b2)
What is the sum of the exterior angles of any polygon?
360 degrees
Always, Sometimes or Never? A parallelogram is a trapezoid.
Never
Rectangle ABCD has two diagonals that bisect at point E. AE = 4x + 5 and BE = 10x - 25. Find x and the length of both diagonals.
x = 5
Diagonal AC and BD are congruent and both equal 50 units.
Always, sometimes, or never? A square is _________ a rhombus.
The diagonals of a kite are...
perpendicular
What is the measure of one interior angle in a regular hexagon?
120 degrees
In parallelogram ABCD, AB = 3x - 4 and CD = x + 8. Find AB.
x = 6
AB = 14
True or False? If a parallelogram is a rectangle, then each diagonal bisects a pair of opposite angles.
False, diagonals bisect each other but they do not bisect a pair of opposite angles.
Rhombus ABCD has opposite angles A and C that have a measure of 110 degrees. What is the angle measure of angles B and D?
B and D are 70 degrees.
If the bases of a trapezoid are 18 and 10, how long is the midsegment?
14
One exterior angle of a regular polygon is 72 degrees. How many sides does this polygon have?
5 sides (pentagon)
Name three properties of parallelograms.
Opposite sides are congruent
Opposite sides are parallel
Consecutive angles are supplementary
Opposite angles are congruent
Diagonals bisect eachother
In rectangle WXYZ, if WY = 5x - 1 and XZ = 2x + 8, what is WY?
x = 3, WY = 14
State two facts about the diagonals of a rhombus.
diagonals are perpendicular and bisect a pair of opposite angles
In kite ABCD, the diagonals intersect at point E and AC is the longer diagonal. If m∠CDE = 40, what is m∠C?
100 degrees