Geometry Notes Lesson 4.2A Properties of Special Quadrilaterals R.4.G.1 Explore and verify the properties of quadrilaterals.

Geometry NotesGeometry NotesLesson 4.2ALesson 4.2A

Properties of Special Properties of Special QuadrilateralsQuadrilaterals

R.4.G.1R.4.G.1 Explore and verify the properties of Explore and verify the properties of quadrilateralsquadrilaterals

TrapezoidsTrapezoids

Definition:Definition:

Bases:Bases:

Legs:Legs:

A quadrilateral with exactly one pair of parallel sides

The parallel sides

The non parallel sides

TrapezoidsTrapezoids

Median of a TrapezoidMedian of a Trapezoid::The segment that joins the midpoints of the legs

median

leg

base

base

leg

B

A

C

D

TrapezoidsTrapezoids

Pairs of Base Angles: Pairs of Base Angles:

Supplementary AnglesSupplementary Angles

medianleg

base

base

leg

B

A

C

D

Located along the same base

Adjacent angles not along the same base

Isosceles TrapezoidIsosceles Trapezoid

Both pairs of base angles of an Both pairs of base angles of an isosceles trapezoid are congruentisosceles trapezoid are congruent

Isosceles TrapezoidIsosceles Trapezoid

The diagonals of an isosceles The diagonals of an isosceles trapezoid are congruenttrapezoid are congruent

Isosceles TrapezoidIsosceles Trapezoid

The median of a trapezoid is parallel The median of a trapezoid is parallel to the bases and measures ½ of the to the bases and measures ½ of the sum of the basessum of the bases

Median = 212

1bb

KitesKites

Definition:Definition:

A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

KitesKites

The diagonals of a kite are The diagonals of a kite are perpendicular. perpendicular.

KitesKites

Segment DE Segment DE Segment BE Segment BE 1 1 22 3 3 44 ABC ABC ADCADC

B

A

D

CE

43 1

2

Example #1Example #1

Find the value of the numbered angles.Find the value of the numbered angles. Find the sum of the angles.Find the sum of the angles. Formula: 180(n-2)Formula: 180(n-2) The angles between the noncongruent sides are equal in The angles between the noncongruent sides are equal in

measure.measure. Let angles 1 and 2 both be x.Let angles 1 and 2 both be x.

53o 47o

1

2

Example #1Example #1

Find the value of the numbered angles.Find the value of the numbered angles. Find the sum of the angles.Find the sum of the angles. Formula: 180(n-2)Formula: 180(n-2) Opposite angles are congruent.Opposite angles are congruent. Adjacent angles are supplementary.Adjacent angles are supplementary.

50o

1

2

Example #2Example #2

Find the value of the variable.Find the value of the variable. The diagonals of a kite are perpendicular.The diagonals of a kite are perpendicular. All four triangles in the kite are right triangles.All four triangles in the kite are right triangles. The sum of the angles in a triangle are 180°.The sum of the angles in a triangle are 180°.

(4x + 9)o

(2x+3)o

Example #2Example #2

Find the value of the variableFind the value of the variable Adjacent angles are supplementary.Adjacent angles are supplementary.

(3x)o (2x)o