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Proof:
In triangles AOB and COD, AO = CO (given) BO = OD (given) (vertically opposite angles are equal) D AOB D COD (SAS congruency condition) Since these are alternate angles made by the transversal AC intersecting AB and CD. AB||CD Similarly, AD||BC Hence ABCD is a parallelogra..
In triangles AOB and COD, AO = CO (given) BO = OD (given) (vertically opposite angles are equal) D AOB D COD (SAS congruency condition) Since these are alternate angles made by the transversal AC intersecting AB and CD. AB||CD Similarly, AD||BC Hence ABCD is a parallelogra..Proof: AB||CD (by definition of parallelogram) AC is a transversal. (alternate angles are equal in a parallelogram) Also AB=DC (opposite sides are equal in a parallelogram) Now in D AOB and D COD, AB=DC (opposite sides of parallelogram are equal) (proved by (i)) D AOB D COD (AAS congruency condi..
AB||CD (by definition of parallelogram) AC is a transversal. (alternate angles are equal in a parallelogram) Also AB=DC (opposite sides are equal in a parallelogram) Now in D AOB and D COD, AB=DC (opposite sides of parallelogram are equal) (proved by (i)) D AOB D COD (AAS congruency condi..Proof:
..
..Proof:
(i) ( Theorem) From (i) and (ii), ..
(i) ( Theorem) From (i) and (ii), ..Proof:
( Linear pair) ( corresponding angles axiom) Similarly, we can prove that..
( Linear pair) ( corresponding angles axiom) Similarly, we can prove that..Proof:
(Vertically opposite angles) From (i) and (ii), ..
(Vertically opposite angles) From (i) and (ii), ..Proof: ( Linear pair) ( corresponding angles axiom) Similarly, we can prove that..
( Linear pair) ( corresponding angles axiom) Similarly, we can prove that..Proof:
(i) [Linear pair (ray FB stands on EFGH)] ( Corresponding angles postulate) (ii) ( given) From (i) and (ii), we have These are corresponding angles. AB ||..
(i) [Linear pair (ray FB stands on EFGH)] ( Corresponding angles postulate) (ii) ( given) From (i) and (ii), we have These are corresponding angles. AB ||..Proof:
( Given) (Vertically opposite angles) (corresponding angles) AB||CD ( corresponding angles axio..
( Given) (Vertically opposite angles) (corresponding angles) AB||CD ( corresponding angles axio..Proof:
i) AD is the median i.e., BD = DC In D ABK, F is the mid-point of AB . (given) G is the mid-point of AK. (by construction) FG || BK or GC || BK ...(1) By theorem on line joining the mid-points of any two sides of a triangle. Similarly in D ACK, GE || CK or GB || CK From (1) and (2)..
i) AD is the median i.e., BD = DC In D ABK, F is the mid-point of AB . (given) G is the mid-point of AK. (by construction) FG || BK or GC || BK ...(1) By theorem on line joining the mid-points of any two sides of a triangle. Similarly in D ACK, GE || CK or GB || CK From (1) and (2)..See what our Users say :
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