parallelogram 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 A..

In triangles, ADE and CEF, AE=EC (given) AD=CF and DE=EF (corresponding parts of corresponding triangles) But AD=DB (given) DB=CF ----(i) (AD is equal to both DB and CF) In quadrilateral DBCF, DB=CF and DB||CF DBCF is a parallelogram. (by definition of parallelogram) ..

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 rhombus is a parallelogram such that AB=DC=AD=BC ---(i) Also the diagonals of a parallelogram bisect each other. Hence BO=DO and AO=OC ---(ii) Now compare triangles AOB and AOD, AB=AD (from (i) above) BO=DO (from (ii) above) AO=AO (common side) (SSS congruency condition) (corr..

In quadrilateral DBCF, DB||CF (by construction) DF||BC (given) DBCF is a parallelogram. DB=CF ----(i) (opposite sides of a parallelogram) But DB=AD ----(ii) (given) From (i) and (ii), AD=CF Now compare triangles, AED and CEF, AD = CF \ AE = EC (CPCT) That is E is the ..

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 parallelogram..

QA || BC and QC || AB by construction. ABCQ is a parallelogram. AQ = BC . . . (1) Similarly BCAR is a parallelogram. AR = BC . . . (2) From (1) and (2), AQ = AR . . . (3) ..

Question 1 - Question: Prove that the area of a trapezium is half the product of its height and the sum of the parallel sides. Answer: Given: ABCD is a trapezium in which AB || DC. Let AB = a, DC = b and CE = AF = h. To prove: Construction: Join AC. Proof: AC is the diagonal of quad. ABCD..

Question: Show that a median of a triangle divides it into two triangles of equal area. Answer: Given: In D ABC, AD is one of the medians of D ABC. To prove: Construction: Draw AE ^ BC. Proof: Since BD = DC and h is the same for both the triang..

Question: Prove that the figure formed by joining the mid-points of pairs of consecutive sides of a quadrilateral is a parallelogram. Answer: Given: ABCD is a quadrilateral. E, F, G and H are the mid-points of AB, BC, CD and DA respectively. To prove: EFGH is a para..