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Directions: Kindly study the following Questions carefully and choose the right answer:
A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC = BD, then the quadrilateral must be a
- a)parallelogram
- b)rhombus
- c)trapezium
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Directions: Kindly study the following Questions carefully and choose ...
The quadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel (in the case AB || CD) is a trapezium.
Hence, option C is correct.
Hence, option C is correct.
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Directions: Kindly study the following Questions carefully and choose ...
Understanding the Problem:
We are given a quadrilateral ABCD that is inscribed in a circle. We are also given that AB is parallel to CD and AC = BD. We need to determine the type of quadrilateral based on the given information.
Key Points:
- A quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary (sum to 180 degrees).
- In a parallelogram, opposite sides are parallel and opposite angles are equal.
- In a rhombus, all sides are equal in length.
- In a trapezium, one pair of opposite sides is parallel.
Solution:
To determine the type of quadrilateral, let's consider the given information and apply the key points mentioned above.
Step 1: Opposite angles in a quadrilateral inscribed in a circle are supplementary.
Since AB is parallel to CD, angle ABC and angle ADC are opposite angles. Similarly, angle BCD and angle BAD are also opposite angles. Since AB is parallel to CD, angle ABC and angle ADC are equal (corresponding angles). Therefore, angle ABC + angle ADC = 180 degrees. Similarly, angle BCD + angle BAD = 180 degrees.
Step 2: Determine the possible types of quadrilaterals based on the given information.
- If opposite angles are equal, the quadrilateral can be a parallelogram.
- If opposite angles are equal and all sides are equal, the quadrilateral can be a rhombus.
- If one pair of opposite sides is parallel, the quadrilateral can be a trapezium.
Step 3: Apply the given information to determine the type of quadrilateral.
Since AB is parallel to CD and angle ABC = angle ADC, we can conclude that angle BCD = angle BAD. This means that opposite angles are equal, satisfying the condition for a parallelogram.
Conclusion:
Based on the given information, we can conclude that the quadrilateral ABCD is a parallelogram. Therefore, option 'C' (trapezium) is incorrect and the correct answer is option 'A' (parallelogram).
We are given a quadrilateral ABCD that is inscribed in a circle. We are also given that AB is parallel to CD and AC = BD. We need to determine the type of quadrilateral based on the given information.
Key Points:
- A quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary (sum to 180 degrees).
- In a parallelogram, opposite sides are parallel and opposite angles are equal.
- In a rhombus, all sides are equal in length.
- In a trapezium, one pair of opposite sides is parallel.
Solution:
To determine the type of quadrilateral, let's consider the given information and apply the key points mentioned above.
Step 1: Opposite angles in a quadrilateral inscribed in a circle are supplementary.
Since AB is parallel to CD, angle ABC and angle ADC are opposite angles. Similarly, angle BCD and angle BAD are also opposite angles. Since AB is parallel to CD, angle ABC and angle ADC are equal (corresponding angles). Therefore, angle ABC + angle ADC = 180 degrees. Similarly, angle BCD + angle BAD = 180 degrees.
Step 2: Determine the possible types of quadrilaterals based on the given information.
- If opposite angles are equal, the quadrilateral can be a parallelogram.
- If opposite angles are equal and all sides are equal, the quadrilateral can be a rhombus.
- If one pair of opposite sides is parallel, the quadrilateral can be a trapezium.
Step 3: Apply the given information to determine the type of quadrilateral.
Since AB is parallel to CD and angle ABC = angle ADC, we can conclude that angle BCD = angle BAD. This means that opposite angles are equal, satisfying the condition for a parallelogram.
Conclusion:
Based on the given information, we can conclude that the quadrilateral ABCD is a parallelogram. Therefore, option 'C' (trapezium) is incorrect and the correct answer is option 'A' (parallelogram).
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Directions: Kindly study the following Questions carefully and choose the right answer:A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC = BD, then the quadrilateral must be aa)parallelogramb)rhombusc)trapeziumd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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