Converse Mid Point Theorem
Converse Mid Point Theorem
Converse of Mid Point Theorem : The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.
GIVEN To Prove E is the mid-point of AC. Construction : Assume F to be mid point of AC. Join DF PROOF As we have assumed F to be the mid-point of AC. Now, in and F is the mid-point of AC. Therefore, by Mid Point Theorem, we have But we are given that , From (i) and (ii) , we find that two intersecting lines DE and DF are both parallel to line BC. This is a contradiction to the parallel line axiom. So, our supposition is wrong. Hence, E is the mid-point of AC. |  |
Illustration:In the figure l,m and n are parallel lines intercepted by two transversal p and q such that l,m and n cut-off equal intercepts AB and BC on p. Show that l,m and n cut off equal intercepts DE and EF on q.
Solution: Join AF meetin BE at G In B is the mid point of AC and BG || CF because it is given that m and n are parallel. By Converse of Mid Point Theorem G is the mid point of AF In G is the mid point of AF and GE || AD because it is given that l and m are parallel. By Converse of Mid Point Theorem E is the mid point of DF Hence DE = EF |  |
E is the midpoint of median AD of | |||
| Right Option : C | |||
| View Explanation | |||
AD and BE are medians of | |||
| Right Option : D | |||
| View Explanation | |||
The converse of mid-point theorem states that : | |||
| Right Option : A | |||
| View Explanation |
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Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
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8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
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