Examples with solutions for Properties, Characteristics and proofs: True / false

Exercise #1

A square has sides measuring 5 cm.

Is AB parallel to CD?

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Video Solution

Step-by-Step Solution

Let's think about the different definitions of different lines.

Looking at side AB and side CD, we can see that if we extend either of them, they will never intersect.

Also, according to the properties of a rectangle, each pair of opposite sides are parallel to each other.

Therefore, the answer is correct and indeed AB is parallel to CD

Answer

Yes

Exercise #2

ABCD is a square with sides measuring 4 cm.


Is ABCD a rectangle?

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Video Solution

Step-by-Step Solution

Since we are given that a square appears in the drawing, we will remember that every pair of opposite sides are parallel.

Let's think about the properties of a rectangle, and remember that in a rectangle, every pair of opposite sides are also parallel.

Therefore, the answer is correct and the quadrilateral ABCD is a rectangle.

Answer

Yes

Exercise #3

A square has side lengths

equal to 4 cm.

Is the distance between BD and AC equal to the length of BD?

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Video Solution

Step-by-Step Solution

Let's think about the properties of a square, remembering that all sides are equal to each other.

In other words, all sides in the square are equal to 4 cm. As a result, we can argue that the distance between BD and AC is indeed equal to 4 since CD is also equal to 4.

Answer

Yes

Exercise #4

A square has sides measuring 5 cm.

Do its diagonals intersect?

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Video Solution

Step-by-Step Solution

Let's think about the properties of a square.

Remember that in a square all sides are equal to each other, meaning all sides are equal to 5 cm.

Also in a square, all angles are equal, they are right angles and equal to 90 degrees.

Therefore, we can claim that the diagonal divides each angle into 2 angles of 45 degrees, thus the diagonals must intersect each other.

Answer

Yes