1. Special Parallelograms
Section 5-4

2. Parallelograms We proved several things by drawing a diagonal
A -- Alternate Interiors
S -- Reflexive
A -- Alternate Interiors
2 Congruent Triangles by ASA

3. 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

4. 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

5. If we stretch the shape to make all sides congruent…
Rhombus – a parallelogram with four congruent sides
-Diagonals are perpendicular
-Diagonals bisect opposite angles

6. Back to parallelograms We can make one of the angles 90˚
Rectangle – parallelogram with all interior angles = 90˚
-Diagonals are congruent

7. 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

8. 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.