Class 10 Exam > Class 10 Questions > Sides AB and BC and median AD of a triangle A...
Start Learning for Free
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?
Most Upvoted Answer
Sides AB and BC and median AD of a triangle ABC are respectively propo...
Community Answer
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.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup