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Geometry
Chapter 7: Proof and Quadrilaterals
7.2.1: Special Quadrilaterals and Proof
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Learning Targets:
n I
can identify parallelograms and kites
based on information about their sides,
angles, and diagonals.
n I
can apply properties of congruent
triangles to prove theorems about
quadrilaterals.
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Mathematical Practice:
n Construct
viable arguments and critique
the reasoning of others.
n Mathematically
proficient students justify
their conclusions.
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CCSSM:
n Prove
geometric theorems.
n Prove
n Make
theorems about parallelograms.
geometric constructions.
n Make
formal geometric constructions
with a variety of tools and methods.
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Quote for today:
n “Iron
rusts from disuse; stagnant water
loses its purity and in cold weather
becomes frozen; even so does inaction
sap the vigor of the mind.”
n Leonardo
da Vinci, (1452 – 1519)
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Corresponding Parts of
Congruent Figures Are
Congruent:
n If
two shapes are congruent, then all
pairs of corresponding parts in the
two shapes are also congruent.
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Quadrilaterals:
n Parallelograms:
n Opposite
sides ____________________
n Opposite
angles ___________________
n Adjacent
angles ___________________
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Quadrilaterals:
n Kites:
n Two
pairs of adjacent, congruent sides.
n One
diagonal bisects a pair of opposite
angles.
n One
diagonal bisects ____________________
n Diagonals
are ___________________________
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Reflexive Property of Equality:
n The
measure of any side or angle is equal to
itself.
n For
example, in the parallelogram below,
because of the reflexive property.
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Assignments:
n WU
7.2.1: Problems 7-97 and 7-98.
n CW
7.2.1: Problems 7-49, 7-51, & 7-52.
n HW
7.2.1: Problems 7-54 and 7-57
through 7-60.