Quadrilaterals Vocab
a rhombus is an equilateral
always
the consecutive angles of a square are supplementary
always
the diagonals of a parallelogram are perpendicular
always
For a rhombus,________________.
each diagonal bisects a pair of opposite angles.(ALWAYS) all four sides are congruent(ALWAYS) the diagonals are congruent(ALWAYS) the diagonals are congruent(NOT ALWAYS)
With a Is triangle ABC a right angle? problem
justify with Pythagorean theorem
For any parallelogram_____________.
opposite sides are congruent (ALWAYS) opposite angles are congruent (ALWAYS) the diagonals bisect each other (ALWAYS) the diagonals are perpendicular (NOT ALWAYS)
All angles of a parallelogram are congruent
sometimes
the diagonals of a rectangle are perpendicular
sometimes
the opposite angles of a rhombus are supplementary
sometimes
For an Isosceles Trapezoid,__________________.
the diagonals are congruent(ALWAYS) the base angles are congruent(ALWAYS) the legs are congruent(ALWAYS) the diagonals are perpendicular(NOT ALWAYS)
Both pairs of opposite angles are congruent
Parallelogram Rectangle Rhombus Square
Both pairs of opposite sides are congruent
Parallelogram Rectangle Rhombus Square
Consecutive angles are supplementary
Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid
SOME RHOMBUSES ARE
RECTANGLES
ALL SQUARES ARE
RHOMBUSES/RECTANGLES
If the diagonals of a parallelogram are congruent, then the parallelogram is also what type of figure?
Rectangle
If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure?
Rhombus
Diagonals of a trapezoid are are congruent
Sometimes
Parallelogram
Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. Diagonals bisect each other. Consecutive angles add to 180 degrees.
Rhombus
Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. Diagonals bisect each other. Consecutive angles add to 180 degrees. All sides are congruent. Diagonals are perpendicular.
Rectangle
Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. Diagonals bisect each other. Consecutive angles add to 180 degrees. Has four right angles. Diagonals are congruent.
Square
Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. Diagonals bisect each other. Consecutive angles add to 180 degrees. Has four right angles. Diagonals are congruent. All sides are congruent. Diagonals are perpendicular.
Opposite sides of a rectangle are congruent
always
How can you use the diagonals to check that a quadrilateral has four right angles?
Diagonals must always be congruent, we can use Pythagorean Theorem to check for concurrency.
Trapezoid
Exactly one pair of parallel sides.
Isosceles Trapezoid
Exactly one pair of parallel sides. One pair of opposite sides are congruent. Diagonals are congruent.
Exactly one pair of opposite sides are congruent
Isosceles Trapezoid
Exactly one pair of opposite angles are congruent
Kite
Opposite angles of an isosceles trapezoid are congruent
Never
Exactly one pair of opposite sides are parallel
Trapezoid
Kite
Two pairs of adjacent sides are congruent. One pair of opposite angles are congruent. Diagonals are perpendicular.