6.2/6.3: Properties of Parallelograms
Can you figure out the puzzle below???
MCE
MCE
MCE
Three Blind Mice
Sides and Angles
Theorem 6.1: Opposite sides of a parallelogram are congruent.
Statements
Reasons
1.
2. AB || DC , BC || AD
3. 1  4, 3  2
4. AC  AC
5. ABC  CDA
1.
2.
6.
6.
3.
4.
5.
Sides and Angles
Consecutive angles: angles of a polygon that share a side
R and S are consecutive angles of a
parallelogram.
They are
.
Theorem 6.2: Opposite angles of a parallelogram are congruent.
Sides and Angles
B
Solve for x and y.
C
( 2 x  10)( y  20)
( 2 x  10)
A
D
Diagonals and Transversals
Theorem 6.3: The diagonals of a parallelogram bisect each other.
Solve a system of linear equations to
find the values of a and b in WXYZ .
Theorem
Theorem 6.5: If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
1
2
Draw diagonal XZ .
3
Statements
Reasons
1.
1.
2. XZ  XZ
3.
4.
5. WX || ZY ,WZ || XY
6.
2.
3. SSS Post.
4. CPCTC
5.
6.
4
Theorem
Theorem 6.6: If both pairs of opposite angles of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
Theorem
Theorem 6.7: If the diagonals of a quadrilateral bisect each other,
then the quadrilateral is a parallelogram.
Theorem
Theorem 6.8: If one pair of opposite sides of a quadrilateral is both
congruent and parallel, then the quadrilateral is a parallelogram.
Applications
Find the values of the variables for which the quadrilaterals must be
parallelograms.
Applications
Determine whether you can prove that the quadrilaterals are
parallelograms. Justify your answer.
6.2/6.3: Properties of Parallelograms
Can you figure out the puzzle below???
pu37-39, 46, 47, 50
HW: p.315 #1-17eiln
odd,
p.324 #1-9 odd, 12-16 even
Line up in alphabetical order