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# Special Parallelograms

Properties of special parallelograms: Rectangle, Rhombus, Square
by

## Ben Whitcomb

on 7 February 2012

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#### Transcript of Special Parallelograms

Opposite sides are congruent
Opposite angles are congruent
Diagonals cut each other in half This is one set of opposite SIDES. They are congruent in ALL parallelograms The top and bottom are also opposite
sides and are congruent This is one set of opposite ANGLES. They are congruent in ALL parallelograms This other pair of opposite angles must also be congruent! BUT! Starting with THIS angle Both of these would
be "consecutive" The YELLOW diagonal splits the Orange diagonal in half Another way of saying that: from the corner to the intersection is the same length This really means "in a row" or "next to" BUT! The Orange diagonal also splits the Yellow diagonal in half Another way of saying that: from the corner to the intersection is the same length The big category is parallelogram But these are all TYPES of parallelograms Which means each still has
THESE properties Rectangle Rhombus Square This is a rectangle. What do we
All four of the corners are RIGHT angles
The diagonals are congruent Remember, this means 90 degrees.
We represent it with a red corner Remember, it is STILL a parallelogram This word means they are the SAME.
So, they have the same length Right Angle Right Angle Right Angle Right Angle

B to D is the same length as A to C All the things that are true for a parallelogram are ALSO true for a rectangle Remember, it is STILL a parallelogram Remember, it is STILL a parallelogram This is a rhombus. What do we
All four sides are congruent
The diagonals meet at a Right angle
The diagonals bisect the angles in half This is a square. What do we
All four of the corners are RIGHT angles
All four of the sides are the same All sides the same length,
but angles don't matter Diagonals meet here,
these center angles are all
Right angles This is a rhombus. If this angle
is 60 degrees Then the diagonal splits it into two 30 degree angles (half the original)

30 Degrees 30 Degrees 60 Degrees All the things that are true for a parallelogram are ALSO true for a rhombus
So, a square is a parallelogram
it is also a rectangle
and it is a rhombus All the things that are true for a parallelogram are ALSO true for a square Use these ideas And use these ideas To solve Problems Example 1 Example 2 Example 3 Problem: JKLM is a rectangle.
The distance from J to K is
50. The distance from J to L is 86. Find LM and HM Problem: TVWX is a Rhombus.
1. Find the distance TV.
2. Also find the measure of angle VTZ Problem: CDFG is a Rhombus. Angle GCD is (b + 3). Angle CDF is (6b - 40). Find the measure of angle GCH JK = 50 JL = 86 Solution: The shape is a rectangle
so it is ALSO a parallelogram. We know
opposite sides of a parallelogram are equal. LM
is opposite KJ, so LM is also 50.

Since the shape is a rectangle, the diagonals are the same length. So, KM is 86 just like JL. The shape is also a parallelogram, so the diagonals cut each other in half. That means HM is half of KM. Half of 86 is 43. HM = 32. The shape is a Rhombus. All the angles in the center are right angles.
The angle at Z measure 90 degrees 14a + 20 = 90 Solve for a. Find a = 5
The top angle XTZ is 5a - 5. 5(5) - 5 = 20 The diagonals split the big angles in
two equal pieces. That means angle VTZ is also 20 Angle CDF Angle GCD Solution: The shape is a rhombus, so it is ALSO a parallelogram. That means the consecutive angles add to 180 degrees. The angles given are consecutive angles. GCD + CDF = 180
b+3 + 6b-40 = 180 Solve for b. Find b = 31 Angle GCD is b+3. Plug in b
31+3=34 We're trying to find GcH. Remember this is a rhombus and CF is a diagonal so it cuts GCD into two equal angles.
GCH is half of 34.
GCH is 17 CF cuts the angle in half The shape is a Rhombus. All the sides are the same.
The highlighted sides are congruent. Set them equal WV = XT 13b-9=3b+4 Solve for b. Find b = 1.3 We know XT = 3b + 4. Put 1.3 in for b
XT = 3*1.3 + 4 = 7.9 The side TV is the same length as all the sides
of the Rhombus, so it is also 7.9 In a house, there are many parallelograms

In the frame

Everything is expected to fit together perfectly When does sombody use this? Did you learn something? Use what you learned to fill in the chart.
Put a check if the property is true A quadrilateral with two pairs of parallel sides All the cool stuff about Rectangles is also true for a Square!
All the stuff about Rhombuses is true for a square too! Squares can do everything
that rectangles do Squares can do everything
that rhombuses do
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