Download Polygon Interior angle sum

POLYGONS ( except Triangles)
Polygon Interior angle sum
The sum of the interior angle measures of an
n-sided convex polygon is (n-2) 180
Polygon Exterior angle sum
The sum of the exterior angle measures of a
convex polygon, one angle at each vertex is
360 degrees
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Parallelograms Theorems
• If the quadrilateral is a parallelogram, then its
opposite sides are congruent.
• If a quadrilateral is a parallelogram, then its
opposite angles are congruent.
• If a quadrilateral is a parallelogram, then its
consecutive angles are supplementary.
• If a parallelogram has one right angle, then it
has four right angles.
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• If a quadrilateral is a parallelogram, then its
diagonals bisect (divides into two equal parts)
each other.
• If a quadrilateral is a parallelogram, then each
diagonal separates the parallelogram into two
congruent triangles.
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Converse of Parallelogram theorems
• If both pairs of opposite side of a quadrilateral
are congruent, then the quadrilateral is a
parallelogram.
• If both pairs of opposite angle of a quadrilateral
are congruent, then the quadrilateral is a
parallelogram.
• If the diagonals of the quadrilateral bisect each
other, then the quadrilateral is a parallelogram.
• If one pair of the opposite sides of a quadrilateral
are both parallel and congruent, then the
quadrilateral is a parallelogram.
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Special Parallelograms and their
theorems
Rectangle
• If the diagonals of a parallelogram are
congruent, then the parallelogram is a
rectangle
• Converse: If the parallelogram is a
rectangle, then their the diagonals are
congruent.
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Rhombus and Square
• If a parallelogram is a rhombus, then its diagonals are
perpendicular.
• If a parallelogram is a rhombus, then each diagonal bisects
pair of opposite angles
• Converse: If the diagonals of a parallelogram are
perpendicular, then the parallelogram is a Rhombus.
• If the diagonal of a parallelogram bisects the opposite
angles, then the parallelogram is a Rhombus
• If one pair of consecutive sides of a parallelogram are
congruent, the parallelogram is a Rhombus
• If a quadrilateral is both a rectangle and a rhombus then, it
is a Square
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Trapezoids and Kites
• If a trapezoid is isosceles, then each pair of base angles is
congruent.
• If a trapezoid has one pair of congruent base angles, then it
is an isosceles trapezoid.
• A trapezoid is isosceles if its diagonals are congruent
• The midsegment of a trapezoid is parallel to each base and
its measure is one half the sum of the length of the bases.
• If a quadrilateral is a kite, then its diagonals are
perpendicular.
• If a quadrilateral is a kite, then exactly one pair of opposite
angles is congruent.
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