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Proof:
( Given) (Vertically opposite angles) (corresponding angles) AB||CD ( corresponding angles axio..
( Given) (Vertically opposite angles) (corresponding angles) AB||CD ( corresponding angles axio..Proof:
(Vertically opposite angles) From (i) and (ii), ..
(Vertically opposite angles) From (i) and (ii), ..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 parallel..
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 parallel..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 (..
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 (..Opposite
In this type, the leaves are arranged in pairs at each node. When the opposite leaves arise in the same plane at successive nodes, it is said to be opposite superposed phyllotaxy. e.g., Quisqualis. When each opposite pair of leaves are at right angles to each..
Proof:
MN is a transversal. (Alternate angles) . . (2) (Alternate angles) From the figure, ( is a straight line and sum of the angles at M = 180 o ) From (1) and (2)..
MN is a transversal. (Alternate angles) . . (2) (Alternate angles) From the figure, ( is a straight line and sum of the angles at M = 180 o ) From (1) and (2)..Proof:
( Linear pair) ( corresponding angles axiom) Similarly, we can prove that..
( Linear pair) ( corresponding angles axiom) Similarly, we can prove that..Proof:
..
..Proof:
(i) ( Theorem) From (i) and (ii), ..
(i) ( Theorem) From (i) and (ii), ..Proof:
AB=AD (sides of a square are equal) AB||DC (opposite sides of a square are parallel) ABCD is parallelogram with consecutive sides equal. ABCD is a rhombus. (by definition) Since the diagonals of a rhombus are perpendicular to each other, AC ^ BD. ABCD is a parallelogram. ABCD is a rectang..
AB=AD (sides of a square are equal) AB||DC (opposite sides of a square are parallel) ABCD is parallelogram with consecutive sides equal. ABCD is a rhombus. (by definition) Since the diagonals of a rhombus are perpendicular to each other, AC ^ BD. ABCD is a parallelogram. ABCD is a rectang..See what our Users say :
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