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Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR?
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Sides AB and BC and median AD of a triangle ABC are respectively propo...
Given:
Triangle ABC with sides AB and BC and median AD proportional to sides PQ and QR and median PM of triangle PQR.
To prove:
Triangle ABC is similar to triangle PQR.
Proof:
1. Proportional Sides:
Let's assume that AB is proportional to PQ and BC is proportional to QR.
If AB is proportional to PQ, then AB/PQ = k (say), where k is a constant. Similarly, BC/QR = k.
Now, let's consider the ratio of the two sides of triangle ABC and triangle PQR.
AB/PQ = BC/QR
Since AB/PQ = BC/QR = k, we can conclude that AB/PQ = BC/QR = AD/PM = k.
2. Median Proportionality:
Given that the median AD is also proportional to the median PM.
AD/PM = k
3. Proportional Triangles:
From the above information, we can conclude that the sides and medians of the two triangles are proportional.
Therefore, triangle ABC is similar to triangle PQR by the rule of similarity.
Conclusion:
Hence, we have proved that triangle ABC is similar to triangle PQR based on the given conditions.
Triangle ABC with sides AB and BC and median AD proportional to sides PQ and QR and median PM of triangle PQR.
To prove:
Triangle ABC is similar to triangle PQR.
Proof:
1. Proportional Sides:
Let's assume that AB is proportional to PQ and BC is proportional to QR.
If AB is proportional to PQ, then AB/PQ = k (say), where k is a constant. Similarly, BC/QR = k.
Now, let's consider the ratio of the two sides of triangle ABC and triangle PQR.
AB/PQ = BC/QR
Since AB/PQ = BC/QR = k, we can conclude that AB/PQ = BC/QR = AD/PM = k.
2. Median Proportionality:
Given that the median AD is also proportional to the median PM.
AD/PM = k
3. Proportional Triangles:
From the above information, we can conclude that the sides and medians of the two triangles are proportional.
Therefore, triangle ABC is similar to triangle PQR by the rule of similarity.
Conclusion:
Hence, we have proved that triangle ABC is similar to triangle PQR based on the given conditions.
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Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR?
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Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR?.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of triangle PQR. Show that triangle ABC ~triangle PQR?.
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