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
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
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