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If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?
- a)no
- b)Yes
- c)Data insufficient
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If sides AB, BC and the median AE in ΔABC is similar to the side...
Given, AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR.
AE and PO are medians, EB = EC and OQ = OR
∵ AE and PO are medians, EB = EC and OQ = OR
∴ Triangles ABE and PQO are similar by SSS as
By property of similar triangles, ∠ABC = ∠PQR
∴ Triangles ABC and PQR are similar by SAS as,
Most Upvoted Answer
If sides AB, BC and the median AE in ΔABC is similar to the side...
Understanding Triangle Similarity
When we talk about triangle similarity, we refer to the concept where two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.
Given Information
- In triangle ABC:
- Sides AB, BC, and median AE are considered.
- In triangle PQR:
- Sides PQ, QR, and median PO are considered.
Condition for Similarity
The given condition states that the sides AB, BC, and median AE in triangle ABC are similar to the sides PQ, QR, and median PO in triangle PQR. This indicates a proportional relationship between the sides and medians of the two triangles.
Why They Are Similar
- Side Proportions: Since AB/ PQ = BC/QR = AE/PO, the sides of both triangles are in proportion.
- Median Relationship: The similarity of the medians (AE and PO) supports the conclusion about the structure of the triangles.
- Angle-Angle (AA) Criterion: If two triangles have their corresponding sides in proportion, the angles will also correspondingly be equal, satisfying the AA criterion for similarity.
Conclusion
Since both the sides and the medians are in proportion, it confirms that triangle ABC is indeed similar to triangle PQR, fulfilling the conditions for triangle similarity.
Final Answer
Thus, the correct answer is: Yes, triangle ABC is similar to triangle PQR.
When we talk about triangle similarity, we refer to the concept where two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.
Given Information
- In triangle ABC:
- Sides AB, BC, and median AE are considered.
- In triangle PQR:
- Sides PQ, QR, and median PO are considered.
Condition for Similarity
The given condition states that the sides AB, BC, and median AE in triangle ABC are similar to the sides PQ, QR, and median PO in triangle PQR. This indicates a proportional relationship between the sides and medians of the two triangles.
Why They Are Similar
- Side Proportions: Since AB/ PQ = BC/QR = AE/PO, the sides of both triangles are in proportion.
- Median Relationship: The similarity of the medians (AE and PO) supports the conclusion about the structure of the triangles.
- Angle-Angle (AA) Criterion: If two triangles have their corresponding sides in proportion, the angles will also correspondingly be equal, satisfying the AA criterion for similarity.
Conclusion
Since both the sides and the medians are in proportion, it confirms that triangle ABC is indeed similar to triangle PQR, fulfilling the conditions for triangle similarity.
Final Answer
Thus, the correct answer is: Yes, triangle ABC is similar to triangle PQR.
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If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
Question Description
If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sides AB, BC and the median AE in ΔABC is similar to the sides PQ, QR and median PO in ΔPQR. State whether ΔABC is similar to, ΔPQR?a)nob)Yesc)Data insufficientd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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