Mid Point Theorem
Mid Point Theorem
MID POINT THEOREM: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
GIVEN A TO PROVE CONSTRUCTION Produce the line segment DE to F, such that DE = EF. Join FC. PROOF In AE = CE [ and, DE = EF [By construction] So, and, As it is given that D is the mid-point of AB
From Eq 2 We know that Now, But they are alternate interior angle when AB and CF are straight lines and DF is the transversal As they are equal so AB || FC , or BD || CF [ When whole are parallel the parts are parallel] Hence BD = CF and BD || CF
But, E is the midpoint of DF [ By construction DE = EF ]
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| Illustration:ABCD is a rhombus, EABF is a straight line such that EA = AB = BF Prove that ED and CF when produced meet at right angle. | |
Proof: ABCD is a rhombus and diagonals of a rhombus bisect at right angle In A is the mid point of EB [ Given EA = AB] O is the mid point of BD [ Diagonals bisect] Now as O and A are mid points of BD and EB . By mid point theorem we can say that ED || AO Similarly In B is the mid point of AF [ Given AB = BF] O is the mid point of AC [ Diagonals bisect] Now as O and B are mid points of AC and AF . By mid point theorem we can say that CF || BO AS BD || FG and AC is the transversal
Similarly EG || AC and GF is the transversal
From (1) and (2) We get
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The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is | |||
| Right Option : B | |||
| View Explanation | |||
In a | |||
| Right Option : C | |||
| View Explanation | |||
The quadrilateral formed by joining the mid - points of the sides of a quadrilateral PQRS, taken in order, is a rhombus if : | |||
| Right Option : D | |||
| View Explanation | |||
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