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A _________ has all the properties of a parallelogram and also that of a kite.
- a)rhombus
- b)quadrilateral
- c)parallelogram
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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A _________ has all the properties of a parallelogram and also that of...
A rhombus has all the properties of a parallelogram and also that of a kite. Let's break down the properties of each shape to understand why a rhombus fits the description.
**Properties of a Parallelogram:**
1. Opposite sides are parallel: In a parallelogram, opposite sides are always parallel. This means that if you extend the sides of a parallelogram, they will never intersect.
2. Opposite sides are congruent: The lengths of opposite sides in a parallelogram are equal. This implies that if you measure the length of one side and compare it to the length of the opposite side, they will be the same.
3. Opposite angles are congruent: The angles formed by the intersection of the sides in a parallelogram are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
4. Consecutive angles are supplementary: The sum of two consecutive angles in a parallelogram is always 180 degrees. For example, if angle A and angle B are consecutive angles in a parallelogram, then angle A + angle B = 180 degrees.
**Properties of a Kite:**
1. Two pairs of adjacent sides are congruent: In a kite, two consecutive sides are equal in length. This means that if you measure the length of one side and compare it to the length of the side next to it, they will be the same.
2. One pair of opposite angles is congruent: The angles formed by the intersection of the sides in a kite are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
3. Diagonals are perpendicular: The diagonals of a kite are perpendicular to each other. This means that if you draw the diagonals of a kite, they will intersect at a right angle.
Based on these properties, a rhombus fits the description of having all the properties of a parallelogram and also that of a kite.
In a rhombus:
- Opposite sides are parallel (parallelogram property).
- Opposite sides are congruent (parallelogram property).
- Opposite angles are congruent (parallelogram property).
- Consecutive angles are supplementary (parallelogram property).
- Two pairs of adjacent sides are congruent (kite property).
- One pair of opposite angles is congruent (kite property).
- Diagonals are perpendicular (kite property).
Therefore, a rhombus is the correct answer as it encompasses all the properties of both a parallelogram and a kite.
**Properties of a Parallelogram:**
1. Opposite sides are parallel: In a parallelogram, opposite sides are always parallel. This means that if you extend the sides of a parallelogram, they will never intersect.
2. Opposite sides are congruent: The lengths of opposite sides in a parallelogram are equal. This implies that if you measure the length of one side and compare it to the length of the opposite side, they will be the same.
3. Opposite angles are congruent: The angles formed by the intersection of the sides in a parallelogram are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
4. Consecutive angles are supplementary: The sum of two consecutive angles in a parallelogram is always 180 degrees. For example, if angle A and angle B are consecutive angles in a parallelogram, then angle A + angle B = 180 degrees.
**Properties of a Kite:**
1. Two pairs of adjacent sides are congruent: In a kite, two consecutive sides are equal in length. This means that if you measure the length of one side and compare it to the length of the side next to it, they will be the same.
2. One pair of opposite angles is congruent: The angles formed by the intersection of the sides in a kite are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
3. Diagonals are perpendicular: The diagonals of a kite are perpendicular to each other. This means that if you draw the diagonals of a kite, they will intersect at a right angle.
Based on these properties, a rhombus fits the description of having all the properties of a parallelogram and also that of a kite.
In a rhombus:
- Opposite sides are parallel (parallelogram property).
- Opposite sides are congruent (parallelogram property).
- Opposite angles are congruent (parallelogram property).
- Consecutive angles are supplementary (parallelogram property).
- Two pairs of adjacent sides are congruent (kite property).
- One pair of opposite angles is congruent (kite property).
- Diagonals are perpendicular (kite property).
Therefore, a rhombus is the correct answer as it encompasses all the properties of both a parallelogram and a kite.
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A _________ has all the properties of a parallelogram and also that of...
Rhombus
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