Characteristics and Proofs of a Rectangle: Identifying and defining elements

Examples with solutions for Characteristics and Proofs of a Rectangle: Identifying and defining elements

Exercise #1

True or false?

One of the angles in a rectangle may be an acute angle.

Video Solution

Step-by-Step Solution

One of the properties of a rectangle is that all its angles are right angles.

Therefore, it is not possible for an angle to be acute, that is, less than 90 degrees.

Answer

False

Exercise #2

Look at the parallelogram ABCD below.

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What can be said about triangles ACD and ABD?

Video Solution

Step-by-Step Solution

According to the side-angle-side theorem, the triangles are similar and coincide with each other:

AC = BD (Any pair of opposite sides of a parallelogram are equal)

Angle C is equal to angle B.

AB = CD (Any pair of opposite sides of the parallelogram are equal)

Therefore, all of the answers are correct.

Answer

All answers are correct.

Exercise #3

Look at the quadrilateral below.

Determine if the quadrilateral is a rectangle.

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Step-by-Step Solution

From the given information, we know that triangle EBC is equilateral.

In an equilateral triangle, all angles are equal to each other.

Therefore, angle B is equal to 60 degrees.

Since none of the angles are 90 degrees, we can safely say that the quadrilateral is not a rectangle.

Answer

It is not a rectangle.

Exercise #4

Given the rectangle, calculate the marked angle

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Video Solution

Answer

120

Exercise #5

Look at the polygon in the diagram.

What type of shape is it?

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Video Solution

Answer

Trapezoid

Exercise #6

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According to the diagram, is the shape a rectangle?

Video Solution

Answer

Yes

Exercise #7

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The quadrilateral ABCD is a square.

Is the square a rectangle?

Video Solution

Answer

Yes.

Exercise #8

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The quadrilateral ABCD above is a rectangle.

The line EF is drawn parallel and equal to BD.

How many rectangles are there in the drawing?

Video Solution

Answer

3

Exercise #9

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Given:

AC=3

BD=3

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According to the data, is it possible to say that the quadrilateral is a rectangle?

Video Solution

Answer

Not true

Exercise #10

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Which sentence is true?

Video Solution

Answer

The diagonals in the rectangle form two pairs of congruent and isosceles triangles.