Which of the following are true about a square?

The diagonals are perpendicular.

Quiz On Rhombus And Square Properties

1.

Which of the following are true about a rhombus?
- A.
  
  The sides are all congruent.
- B.
  
  The diagonals are congruent.
- C.
  
  It has four right angles.
- D.
  
  All of the above.
Correct Answer
A. The sides are all congruent.

Explanation
A rhombus is a quadrilateral with all four sides congruent. This means that all the sides of a rhombus have the same length. The other statements in the question, such as the diagonals being congruent and the rhombus having four right angles, are not necessarily true for all rhombuses. Therefore, the correct answer is that the sides are all congruent.

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2.

Which of the following are true about a square?
- A.
  
  The diagonals are congruent.
- B.
  
  The sides are congruent.
- C.
  
  It has four right angles.
- D.
  
  The diagonals are perpendicular.
- E.
  
  All of the above.
Correct Answer
E. All of the above.

Explanation
A square is a quadrilateral with four equal sides and four right angles. The diagonals of a square are congruent, meaning they have the same length. Additionally, the diagonals of a square are perpendicular to each other, forming right angles where they intersect. Therefore, all of the statements mentioned in the options are true about a square.

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3.

In the rhombus below, what is the length of HO?

Correct Answer
8
4.

In the rhombus below, what would be the perimeter of the figure? (The perimeter is found by adding the lengths of all of the sides together.)

Correct Answer
32

Explanation
The perimeter of a rhombus is found by adding the lengths of all of its sides together. Since the answer is given as 32, it suggests that each side of the rhombus has a length of 8. Therefore, the perimeter would be 8 + 8 + 8 + 8 = 32.

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5.

In the rhombus below, what angle is formed by the diagonals in degrees?

Correct Answer
90

Explanation
A rhombus is a quadrilateral with all sides equal in length. In a rhombus, the diagonals bisect each other at right angles, meaning they form 90-degree angles. Therefore, the angle formed by the diagonals in a rhombus is always 90 degrees.

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6.

In the square below, what angle is formed by the diagonals in degrees, angle BEC?

Correct Answer
90

Explanation
The angle formed by the diagonals in a square is always 90 degrees. This is because a square has four equal sides and four right angles, so the diagonals bisect each other at right angles, resulting in a 90-degree angle.

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7.

In the square below, what is the measure of angle B in degrees?

Correct Answer
90

Explanation
The measure of angle B in a square is always 90 degrees. In a square, all angles are equal and all sides are equal in length. Therefore, angle B will always be 90 degrees.

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8.

In the square below, if AB = 12, what is the length of AD?

Correct Answer
12

Explanation
The square is symmetrical, so the length of AD will be equal to the length of AB, which is given as 12.

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9.

In the square below, if AE = 8, what is the measure of BE?

Correct Answer
8

Explanation
Since AE = 8 and AE is a side of the square, it means that the length of each side of the square is 8 units. Therefore, BE, which is also a side of the square, will also have a length of 8 units.

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10.

In the rhombus below, find the missing angle using the fact that the diagonals are perpendicular.

Correct Answer
35

Explanation
Since the diagonals of a rhombus are perpendicular, the opposite angles are congruent. Therefore, if one angle is 35 degrees, the opposite angle must also be 35 degrees.

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