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 |  |
S and Q are the mid-point of AD and BC respectively. So, parallel line to AC must intersect for both S and Q at the mid-points of ____ and ____. | |||
| Right Option : B | |||
| View Explanation | |||
The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the __________ at its mid-point. | |||
| Right Option : C | |||
| View Explanation | |||
ABCD is a trapezium.in which side AB is parallel to side DC and E is the mid-point of AD. So, EF must intersect BC at ______ . | |||
| Right Option : B | |||
| View Explanation | |||
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