Download Special Parallelograms

Special Parallelograms
Section 5-4
Parallelograms
We proved several things by drawing a diagonal
A -- Alternate Interiors
S -- Reflexive
A -- Alternate Interiors
2 Congruent Triangles by ASA
Parallelograms
We proved several things by drawing a diagonal
Since we have congruent triangles we can prove other pieces
congruent by CPCTC:
1.) Opposite Sides Congruent
2.) Opposite Angles Congruent
3.) Diagonals Bisect Each Other
If we stretch the shape to make all
sides congruent…
This is still a parallelogram, so diagonals bisect each other
Now we have four congruent triangles by SSS
If we stretch the shape to make all
sides congruent…
Rhombus – a parallelogram with four congruent sides
-Diagonals are perpendicular
-Diagonals bisect opposite angles
Back to parallelograms
We can make one of the angles 90˚
Rectangle – parallelogram with all interior angles = 90˚
-Diagonals are congruent
Diagonal Theorems
• Theorem 5-12 – The diagonals of a
rectangle are congruent
• Theorem 5-13 – The diagonals of a
rhombus are perpendicular
• Theorem 5-14 – Each diagonal of a
rhombus bisects two angles of the
rhombus
More Theorems
• 5-15 – The midpoint of the hypotenuse of
a right triangle is equidistant from the three
vertices
• 5-16 – If one angle of a parallelogram is a
right angle, then the parallelogram is a
rectangle
• 5-17 – If two consecutive sides of a
parallelogram are congruent, then the
parallelogram is a rhombus.