Download Geometry Chapter 6 - Hudson Falls Middle School

Geometry Chapter 6
By: Cate Hogan, Austin Underwood,
Paige Mager
Classifying Quadrilaterals
• Parallelogram: A quadrilateral with both pairs of
opposite sides being parallel
• Rhombus: A parallelogram with four congruent sides
• Rectangle: parallelogram with four right angles
• Square: parallelogram with four congruent sides and
four right angles
• Kite: a quadrilateral with two pairs of adjacent sides
congruent and no opposite sides congruent
• Trapezoid: a quadrilateral with exactly one pair of
opposite sides
Properties of Parallelograms
• Opposite sides of a parallelogram are
congruent
• Opposite sides are congruent
• Opposite angles are congruent
• Consecutive angles are supplementary
• Diagonals bisect each other
• Diagonals form two congruent triangles
Proving That a Quadrilateral is a
Parallelogram
• If both pairs of opposite sides of a quadrilateral are
congruent, it is a parallelogram
• If both pairs of opposite angles of a quadrilateral are
congruent, it is a parallelogram
• If the diagonals of a quadrilateral bisect each other, it
is a parallelogram
• If one pair of opposite sides of a quadrilateral is both
congruent and parallel, then it is a parallelogram
Special Parallelograms
• Rhombus:
– If one diagonal bisects two angles of a
parallelogram, then the parallelogram is a rhombus
– If the diagonals of a parallelogram are
perpendicular, then the parallelogram is a rhombus
• Rectangle:
– If the diagonals of a parallelogram are congruent,
then the parallelogram is a rectangle
• Square:
– Combine properties previously mentioned in the
slide
Trapezoids and Kites
• Trapezoid:
– Base sides are parallel
– The two pairs of angles between the bases are
supplementary
• Isosceles trapezoid:
– Look at properties of a trapezoid
– Base angles are congruent
– Diagonals are congruent
• Kite:
– Diagonals are perpendicular
– Side angles are congruent
– Vertical diagonals form two congruent triangles
– Diagonals bisect top and bottom angles
Placing figures in the Coordinate
Plane
• Consecutive points should be connected
segments of the shape
Proofs Using Coordinate Geometry
• The midsegment of a trapezoid is parallel to
the bases
• The length of a midsegment of a trapezoid is
(b +b )
2
1
2
Citations
•
•
•
Prentice Hall Mathematics
Geometry Textbook
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