Quadrilaterals Vocab

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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.


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