# When GIVEN a parallelogram, the definition and theorems are stated as ...

Ηλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 4 χρόνια και 9 μήνες)

155 εμφανίσεις

When GIVEN a parallelogram, the definition and theorems
are stated as ...

A
parallelogram

is a quadrilateral with both pairs of opposite sides
parallel.

If a quadrilateral is a parallelogram, the
2 pairs of opposite sides are
congruent.

If a quadrilateral is a parallelogram, the
2 pairs of opposite angles are
congruent.

If a quadrilateral is a parallelogram, the
consecutive angles are
supplementary.

If a quadrilateral is a parallelogram, the
diagonals bisect each other.

If a quadrilateral is a parallelogram, the
diagonals form two
congruent triangles.

When trying to PROVE a parallelogram, the definition and
theorems are stated as ...

(many of these theorems are converses of the previous theorems)

A
parallelogram

is a quadrilateral with both pairs of opposite sides
parallel.

If both pairs of opposite sides
of a quadrilateral are congruent, the
quadrilateral is a parallelogram.

If both pairs of opposite angles of a quadrilateral are congruent, the
quadrilateral is a parallelogram.

If

one angle is supplementary to both consecutive angles in a

If the diagonals of a quadrilateral bisect each other, the quadrilateral
is a parallelogram.

If ONE PAIR of opposite sides of a quadrilateral are BOTH parallel
and congruent, the quadrilateral is a parallelogram.

**

Be sure to remember this last met
hod, as it may save you time when
working a proof.

Proof of Theorem:

If a quadrilateral is a parallelogram, the
2 pairs of
opposite sides are congruent.

(
Remember:

when attempting to prove a theorem to be true,

you cannot use the theorem as a reason

STATEMENTS

REASONS

1

1

Given

2

Draw segment from

A

to
C

2

Two points determine exactly one line.

3

3

A
parallelogram

is a quadrilateral with both
pairs of opposite sides parallel.

4

4

If two parallel li
nes are cut by a transversal,
the alternate interior angles are congruent.

5

5

Reflexive property:

A quantity is congruent
to itself.

6

6

ASA:

If two angles and the included side of
one triangle are congruent to the
corresponding parts of another triangle, the
triangles are congruent.

7

7

CPCTC:

Corresponding parts of congruent
triangles are congruent.

Proof of Theorem:

If
ONE PAIR

of opposite sides of a quadrilateral
are
BOTH

par
allel and congruent, the quadrilateral is a parallelogram.

(
Remember:

when attempting to prove a theorem to be true,

you cannot use the theorem as a reason in your proof.)

STATEMENTS

REASONS

1

1

Given

2

Draw segment from

A

to
C

2

Two points determine exactly one line.

3

3

If two parallel lines are cut by a transversal,
th
e alternate interior angles are congruent.

4

4

Reflexive property:

A quantity is congruent
to itself.

5

5

SAS~SAS:

If two sides and the included
angle of one triangle are congruent to the
corresponding parts of another triangle, the
triangles are congruent.

6

6

CPCTC:

Corresponding parts of congruent
triangles are congruent.

7

7

If two lines are cut by a transversal and the
alternate interior angles are congruent, the
lines are parallel.

8

8

A
parallelogram