6.3 - KTL MATH CLASSES
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Transcript 6.3 - KTL MATH CLASSES
Chapter 6
Section 6.3
Proving Quadrilaterals Are Parallelograms
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Quick Review
Some Properties of Parallelograms
Definition: A parallelogram is a quadrilateral with both
pairs of opposite sides congruent
If a quadrilateral is a parallelogram, then …
Theorem 6.2
both pairs of opposite sides are congruent
Theorem 6.3
both pairs of opposite angles are congruent
Theorem 6.4
consecutive angles are supplementary
Theorem 6.5
diagonals bisect each other
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Theorem
Theorem 6.6
If both pairs of opposite sides of a quadrilateral
are congruent, then the quadrilateral is a parallelogram
Quadrilateral PQRS with both pairs of opposite sides
congruent
PQRS is a parallelogram
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Theorem
Theorem 6.7
If both pairs of opposite angles of a quadrilateral
are congruent, then the quadrilateral is a parallelogram
Quadrilateral PQRS with both pairs of opposite
angles congruent
PQRS is a parallelogram
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Theorem
Theorem 6.8
If an angle of a quadrilateral is supplementary to both
of its consecutive angles, then the quadrilateral is
a parallelogram
mS + mP = 180 and mS + mR = 180
PQRS is a parallelogram
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Theorem
Theorem 6.9
If the diagonals of a quadrilateral bisect each other,
then the quadrilateral is a parallelogram
PR bi sec ts QS and QS bi sec ts PR
PQRS is a parallelogram
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Theorem
Theorem 6.10
If one pair of opposite sides of a quadrilateral are congruent
and parallel, then the quadrilateral is a parallelogram
PQ // SR and PQ SR
PQRS is a parallelogram
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Yes, one pair of opposite
sides congruent and
parallel
Yes, diagonals bisect each other
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Yes, both pairs of opposite
sides congruent
No, same pair of opposite sides
must be parallel and congruent
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Yes, could show both pairs
of opposite sides are
parallel
Yes, Consecutive angles are
supplementary
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Definition: AD || BC
Theorem 6.10: AB DC
Theorem 6.6: AD BC
Theorem 6.10: AB || DC
AB || DC
Definition: AD || BC
Theorem 6.10: AB DC
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
Theorem 6.9: AE EC
Theorem 6.8: mCDA + mDCB = 180
OR
mDAB + mABC = 180
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
For a Quadrilateral to be a
parallelogram opposite sides
must be congruent
3x = 6
x=2
x+2=y-1
2+2=y–1
4=y–1
5=y
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
For a Quadrilateral to be a
parallelogram opposite angles
must be congruent
2x = 70
x = 35
3x + 5 = x + 3y
3(35) + 5 = 35 + 3y
110 = 35 + 3y
75 = 3y
25 = y
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
For a Quadrilateral to be a
parallelogram diagonals must
bisect each other
3x = 12
x=4
x + y = 5y
4 + y = 5y
4 = 4y
1=y
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
2. Def. ’s
Proving Quadrilaterals are Parallelograms
Lesson 6.3
Proving a Quad is a Parallelogram
2. Def. ’s
Proving Quadrilaterals are Parallelograms
Lesson 6.3
HW #68
Pg 342-345 10-26 Even, 30, 32, 34-37
Proving Quadrilaterals are Parallelograms
Lesson 6.3