Class 9 Exam > Class 9 Questions > Assertion (A): In the adjoining figure, X and...
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Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sides
AB and AC of ΔABC such that AX = AY then CX = BY.
Reason(R): If two sides and the included angle of one triangle are equal to two sides and
the included angle of the other triangle, then the two triangles are congruent.?
AB and AC of ΔABC such that AX = AY then CX = BY.
Reason(R): If two sides and the included angle of one triangle are equal to two sides and
the included angle of the other triangle, then the two triangles are congruent.?
Verified Answer
Assertion (A): In the adjoining figure, X and Y are respectively two p...
The assertion (A) and reason (R) are both true.
In the given figure, if X and Y are points on equal sides AB and AC of triangle ABC such that AX = AY, then it can be concluded that triangles AXY and ABC are similar triangles. This is because they have two equal sides and the included angle.
According to the reason (R), if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent. Since triangles AXY and ABC are similar, it can be concluded that they are also congruent.
Therefore, as a result of congruence, we have that CX = BY.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
Assertion (A): In the adjoining figure, X and Y are respectively two p...
The given figure and statement are as follows:
Given figure:
B
/ \
/ \
/ \
/ \
/ \
A-----------C
Statement:
In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ΔABC such that AX = AY, then CX = BY.
To prove:
CX = BY
Proof:
Step 1: Draw a line segment XY to complete the triangle AXY.
B
/ \
/ \
/ \
/ \
/ \
A-----------C
\ /
\ /
\ /
\ /
\/
X Y
Step 2: In triangles ABC and AXY,
- AX = AY (Given)
- AB = AC (Given)
- ∠B = ∠Y (Vertically opposite angles)
Therefore, by the ASA congruence rule, triangles ABC and AXY are congruent.
Step 3: By the congruence of triangles ABC and AXY,
- CX = XY (Corresponding parts of congruent triangles are congruent)
- BY = XY (Corresponding parts of congruent triangles are congruent)
Therefore, CX = BY
Conclusion:
Using the ASA congruence rule, we can conclude that if X and Y are two points on equal sides AB and AC of triangle ABC such that AX = AY, then CX = BY.
Given figure:
B
/ \
/ \
/ \
/ \
/ \
A-----------C
Statement:
In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ΔABC such that AX = AY, then CX = BY.
To prove:
CX = BY
Proof:
Step 1: Draw a line segment XY to complete the triangle AXY.
B
/ \
/ \
/ \
/ \
/ \
A-----------C
\ /
\ /
\ /
\ /
\/
X Y
Step 2: In triangles ABC and AXY,
- AX = AY (Given)
- AB = AC (Given)
- ∠B = ∠Y (Vertically opposite angles)
Therefore, by the ASA congruence rule, triangles ABC and AXY are congruent.
Step 3: By the congruence of triangles ABC and AXY,
- CX = XY (Corresponding parts of congruent triangles are congruent)
- BY = XY (Corresponding parts of congruent triangles are congruent)
Therefore, CX = BY
Conclusion:
Using the ASA congruence rule, we can conclude that if X and Y are two points on equal sides AB and AC of triangle ABC such that AX = AY, then CX = BY.
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Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.?
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Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? 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 Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.?.
Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? 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 Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.?.
Solutions for Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? in English & in Hindi are available as part of our courses for Class 9.
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Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.?, a detailed solution for Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? has been provided alongside types of Assertion (A): In the adjoining figure, X and Y are respectively two points on equal sidesAB and AC of ΔABC such that AX = AY then CX = BY.Reason(R): If two sides and the included angle of one triangle are equal to two sides andthe included angle of the other triangle, then the two triangles are congruent.? theory, EduRev gives you an
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