Properties, Characteristics and proofs: Parallelogram within a square

Examples with solutions for Properties, Characteristics and proofs: Parallelogram within a square

Exercise #1

Look at the square below:

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Is AF equal to ED?

Video Solution

Step-by-Step Solution

Since it is not given that FD is parallel to AE, it cannot be argued that AF is necessarily equal to ED

Answer

No

Exercise #2

The square ABCD and the parallelogram AFED are shown below.

The area of the parallelogram is equal to 100.

ED = 5

How long is AC?

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Video Solution

Step-by-Step Solution

The area of a parallelogram is equal to the side multiplied by the height, as we know that ED is equal to 5, the area is also given.

We place the data in the following formula:

S=AC×ED S=AC\times ED

100=AC×5 100=AC\times5

We divide by 5 the two sections:

1005=5AC5 \frac{100}{5}=\frac{5AC}{5}

20=AC 20=AC

Answer

20 20

Exercise #3

In the square ABCD, side FD is parallel to side AE.

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Is AF equal to ED?

Video Solution

Answer

Yes

Exercise #4

The parallelogram AFED is drawn inside the square ABCD.

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Are the areas of triangles ACE and FBD equal?

Video Solution

Answer

Yes

Exercise #5

Square ABCD and parallelogram AFED are shown below.

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Is side AE a bisector?

Video Solution

Answer

No

Exercise #6

Square ABCD and parallelogram AFED are shown below.

Parallelogram AFED has an area equal to 4.

AC=4 AC=4

How long is side ED?

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Video Solution

Answer

1 1

Exercise #7

Square ABCD and parallelogram AFED are shown below.

The area of the parallelogram is equal to 64.

AF=4 AF=4

How long is side AC?

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Video Solution

Answer

16 16