Special Parallelogarms What do we already know about parallelograms?

Opposite sides are congruent

Opposite angles are congruent

Consecutive angles add to 180

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

know about it?

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

know about it?

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

know about it?

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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# Special Parallelograms

Properties of special parallelograms: Rectangle, Rhombus, Square

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