1. The document discusses different types of parallelograms including rectangles, rhombuses, and their properties. 2. Key properties include diagonals bisecting each other in parallelograms, diagonals being congruent in rectangles, and diagonals being perpendicular in rhombuses. 3. Theorems are presented about the properties of parallelograms including their angles and diagonals.

1. Special Parallelograms
Section 5-4

2. Activity: JUMBLED LETTERS
Directions: Arrange the following jumbled letters using
the given hint below. Write the correct word/s on a
separate answer sheet.
1. It is a shape of Sponge Bob’s pants.
2. Its shape looks like a chalkboard.

3. 3. Its shape looks like a diamond.
4. These are two line segments meeting at a point
forming right angle. It has a symbol of .

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

6. 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
Parallelograms
We proved several things by drawing a diagonal

7. 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

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

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

10. 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

11. 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.