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In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?
1. QR = 5XY
2. QR is parallel to XY
3. Triangle PYX is similar to triangle PRQ
1. QR = 5XY
2. QR is parallel to XY
3. Triangle PYX is similar to triangle PRQ
Q. Select the correct answer using the code given below.
- a)1 and 2 only
- b)2 and 3 only
- c)1 and 3 only
- d)1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a triangle PQR, point X is on PQ and point Y is on PR such that XP ...
PQ = XQ + PX = 6 + 1.5 = 7.5 units
PR = PY + YR = 2 + 8 = 10 units
In triangle PXY and PQR
⇒ PX/PQ = 1.5/7.5 = 1/5
⇒ PY/PR = 2/10 = 1/5
⇒ PX/PQ = PY/PR
∠P is common
⇒ PXY ∼ PQR [SAS ∼]
⇒ XY/QR = PX/PQ = 1/5
⇒ 5XY = QR
⇒ Statement I is true.
In triangle PQR
⇒ PX/XQ = ¼ = PY/YR
⇒ QR is parallel to XY [∵ Inverse BPT theorem]
⇒ Statement II is true.
∴ All the statements are true.
Most Upvoted Answer
In a triangle PQR, point X is on PQ and point Y is on PR such that XP ...
Given Information:
- XP = 1.5 units, XQ = 6 units
- PY = 2 units, YR = 8 units
Explanation:
1. QR = 5XY:
- Using the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- In triangle PQR, PQ + QR > PR, PQ + PR > QR, and QR + PR > PQ.
- Substitute the given values: 1.5 + 6 > QR, 1.5 + QR > 6, 6 + QR > 1.5
- Solving these inequalities, we get QR > 4.5, QR < 7.5,="" and="" qr="" /> 4.5
- Therefore, QR can be any value between 4.5 and 7.5. So, QR is not necessarily equal to 5XY.
2. QR is parallel to XY:
- Since QR is a side of triangle PQR and XY is not a side of the same triangle, QR cannot be parallel to XY.
3. Triangle PYX is similar to triangle PRQ:
- By Angle-Angle (AA) similarity theorem, if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
- Angle PYX is congruent to angle PRQ (both are right angles).
- Angle PXY is congruent to angle PQR (both are common angles).
- Therefore, triangle PYX is similar to triangle PRQ.
Therefore, the correct answer is option 'D' as none of the statements 1, 2, and 3 are correct.
- XP = 1.5 units, XQ = 6 units
- PY = 2 units, YR = 8 units
Explanation:
1. QR = 5XY:
- Using the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- In triangle PQR, PQ + QR > PR, PQ + PR > QR, and QR + PR > PQ.
- Substitute the given values: 1.5 + 6 > QR, 1.5 + QR > 6, 6 + QR > 1.5
- Solving these inequalities, we get QR > 4.5, QR < 7.5,="" and="" qr="" /> 4.5
- Therefore, QR can be any value between 4.5 and 7.5. So, QR is not necessarily equal to 5XY.
2. QR is parallel to XY:
- Since QR is a side of triangle PQR and XY is not a side of the same triangle, QR cannot be parallel to XY.
3. Triangle PYX is similar to triangle PRQ:
- By Angle-Angle (AA) similarity theorem, if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
- Angle PYX is congruent to angle PRQ (both are right angles).
- Angle PXY is congruent to angle PQR (both are common angles).
- Therefore, triangle PYX is similar to triangle PRQ.
Therefore, the correct answer is option 'D' as none of the statements 1, 2, and 3 are correct.
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In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?
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In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct?1. QR = 5XY2. QR is parallel to XY3. Triangle PYX is similar to triangle PRQQ. Select the correct answer using the code given below.a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
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