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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer as
Assertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BC
Reason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilateral
- a)Both assertion and reason are true and reason is the correct explanation of assertion.
- b)Both assertion and reason are true but reason is not the correct explanation of assertion.
- c)Assertion is true but reason is false.
- d)Assertion is false but reason is true.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of Assertion is gi...
To prove DE || BC
i.e., ∠B ∠ADE .
In Δ ABC , we have
AB = AC
∠B = ∠C ...(1)
In the cyclic quadrilateral CBDE , side BD is produced to A. We know that an exterior angle of cyclic quadrilateral is equal to interior opposite angle of cyclic quadrilateral.
∠ADE = ∠C ...(2)
From (1) and (2), we get
∠B = ∠ADE .
Hence, DE || BC
Most Upvoted Answer
Direction: In the following questions, a statement of Assertion is gi...
Assertion: In an isosceles triangle ABC with AB = AC, a circle passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BC.
Reason: The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle of that quadrilateral.
Explanation:
To prove that DE || BC, we need to show that the alternate interior angles formed by DE and BC are equal.
Step 1: Draw the figure and label the given information.
Given: Isosceles triangle ABC with AB = AC, a circle passing through B and C intersects the sides AB and AC at D and E respectively.
Let's draw the figure:
A
/ \
/ \
B-----C
\ /
\ /
D
|
E
Step 2: Understand the given information.
We are given that triangle ABC is an isosceles triangle with AB = AC. Also, a circle passing through B and C intersects the sides AB and AC at points D and E respectively.
Step 3: Identify the relevant properties.
Since the circle passing through B and C intersects AB and AC, we can say that angles ABD and ACE are inscribed angles.
According to the property of inscribed angles, the measure of an inscribed angle is half the measure of its intercepted arc.
So, angle ABD = 1/2 arc AC and angle ACE = 1/2 arc AB.
Step 4: Apply the given reason.
The reason given states that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle of that quadrilateral.
In this case, the quadrilateral ABCD is cyclic because it is inscribed in a circle. So, angle ABD is an exterior angle and angle ACE is the interior opposite angle.
According to the reason, angle ABD = angle ACE.
Step 5: Conclude the proof.
Since angle ABD = angle ACE, we can say that DE is parallel to BC. Therefore, the assertion is true and the reason is the correct explanation of the assertion.
Hence, the correct answer is option 'A' - Both assertion and reason are true and the reason is the correct explanation of the assertion.
Reason: The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle of that quadrilateral.
Explanation:
To prove that DE || BC, we need to show that the alternate interior angles formed by DE and BC are equal.
Step 1: Draw the figure and label the given information.
Given: Isosceles triangle ABC with AB = AC, a circle passing through B and C intersects the sides AB and AC at D and E respectively.
Let's draw the figure:
A
/ \
/ \
B-----C
\ /
\ /
D
|
E
Step 2: Understand the given information.
We are given that triangle ABC is an isosceles triangle with AB = AC. Also, a circle passing through B and C intersects the sides AB and AC at points D and E respectively.
Step 3: Identify the relevant properties.
Since the circle passing through B and C intersects AB and AC, we can say that angles ABD and ACE are inscribed angles.
According to the property of inscribed angles, the measure of an inscribed angle is half the measure of its intercepted arc.
So, angle ABD = 1/2 arc AC and angle ACE = 1/2 arc AB.
Step 4: Apply the given reason.
The reason given states that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle of that quadrilateral.
In this case, the quadrilateral ABCD is cyclic because it is inscribed in a circle. So, angle ABD is an exterior angle and angle ACE is the interior opposite angle.
According to the reason, angle ABD = angle ACE.
Step 5: Conclude the proof.
Since angle ABD = angle ACE, we can say that DE is parallel to BC. Therefore, the assertion is true and the reason is the correct explanation of the assertion.
Hence, the correct answer is option 'A' - Both assertion and reason are true and the reason is the correct explanation of the assertion.
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?.
Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer asAssertion : In an isosceles triangles ABC with AB = AC , a circle is passing through B and C intersects the sides AB and AC at D and E respectively. Then DE || BCReason : Exterior angle of a cyclic quadrilateral is equal to interior opposite angle of that quadrilaterala)Both assertion and reason are true and reason is the correct explanation of assertion.b)Both assertion and reason are true but reason is not the correct explanation of assertion.c)Assertion is true but reason is false.d)Assertion is false but reason is true.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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