Midsegments of a Triangle

Lesson 7: QUADRILATERALS

5.7.1: Parallelograms (Parallelogram, Square, Rectangle, Rhombus)

5.7.2: Special Quadrilaterals (Trapezoid, Kite)

All Quadrilateral have 4 sides and the sum of the measures of the angles is 360

PARALLELOGRAMSA quadrilateral is a parallelogram if:

• Opposite sides are parallel

• Opposite sides are congruent

• Opposite angles are congruent

• Consecutive angles are supplementary

• The diagonal forms two congruent triangles

• Diagonals bisect each other

RECTANGLES A rectangle is a parallelogram:

• Opposite sides parallel

• Opposite sides congruent

• All 4 angles are right angles

• Diagonals bisect each other

• Diagonals are congruent

SQUARESA square is a parallelogram:

• All sides congruent

• All right angles

• Opposite sides parallel

• Congruent diagonals

• Diagonals bisect each other

• Diagonals bisect opposite angles

• Diagonals are perpendicular

RHOMBUSES A rhombus is a parallelogram:

• 4 congruent sides

• Opposite sides parallel

• Consecutive angles are supplementary

• Diagonals bisect each other

• Diagonals bisect opposite angles

• Diagonals are perpendicular

TRAPEZOIDSA trapezoid:

• NOT a parallelogram

• 1 set of opposite sides are parallel

• Parallel sides are called bases, nonparallel sides are called legs

• The midesegment is the average of the two parallel sides

ISOSCELES TRAPEZOIDSAn isosceles trapezoid:

• NOT a parallelogram

• Bases are parallel

• Legs are congruent

• Base angles are congruent

• Diagonals are congruent

• The midsegment is the average of the two parallel sides

KITESA kite:

• NOT a parallelogram

• 2 pairs of congruent sides that are adjacent

• The angles between the 2 noncongruent sides are congruent

• Diagonals are pependicular

• One of the diagonals is beisected