Which quadrilaterals always have diagonals that are congruent?
Rectangles and squares
All quadrilaterals are parallelograms.
False
Find m<PQR in the Rhombus.
m<PQR=120
A square is a rectangle.
Always
How many types of special parallelograms did we learn about?
3
Which quadrilaterals always have diagonals that are perpendicular?
Rhombuses and squares
A parallelogram with 4 right angle is always a rectangle.
True
x = 1
y = 1/2
A rectangle is a square.
Sometimes
What were 2 properties we used to prove parallelograms based on their sides?
Parallel & congruent
Which quadrilaterals have diagonals that DO NOT bisect opposite angles?
Rectangles and parallelograms
All rhombuses are squares
False
Find the value of z & w in the parallelogram.
z = 11, w = 4.5
9z+19=11z-3, 19=2z-3, 22=2z, z=11
plug in 11 ... m<H= 11(11)-3 = 118
m<G + m<H = 180, so m<G=62
solve ... 14w-1=62, w=4.5
A rectangle has perpendicular diagonals.
Sometimes
How many properties are shared between all the special parallelograms? Then name them.
5:
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
Which quadrilaterals always have diagonals that bisect each other?
Parallelograms, rectangles, rhombuses, and squares
A parallelogram with perpendicular diagonals is a rhombus.
True
Find WZ if VZ= 6 and WX = 10
WZ = 8
62 + (WZ)2 = 102
A parallelogram has diagonals that bisect each other.
Always
Classify the quadrilateral if possible and explain your thinking.
Diagonals bisect each other making it at least a parallelogram, but they are also perpendicular meaning it must be a rhombus.
Which quadrilaterals always have consecutive angles that are supplementary?
Parallelograms, rectangles, rhombuses, and squares
A parallelogram with four congruent sides is a square.
False
If the figure is a square find the measure of each angle.
m<1=90 m<2=m<3=m<4=m<5 = 45
Since diagonals are congruent, perpendicular, and bisect each other the individual triangles are all right isosceles triangle. Also the corners are 90 degrees and the diagonals bisect those angles.
The angle measures in each are 45, 45, & 90 degrees.
The diagonals of a rhombus are perpendicular.
Always
Classify the quadrilateral if possible, explain your thinking.
Not enough information, we would need another 90 degree angle to get some parallel sides or more sides congruent.