Parallelograms on the same base and between the same parallels are equal in area. Given: Two parallelograms ABCD and EFCD, are on the same base DC and between the same parallel lines AF and DC. To prove: area (∥gm ABCD) = area (∥gm EFCD) Proof: In △ AED and △ BFC BC ∥ AD and AF is a transversal.So, ∠DAE = ∠CBF …..(1) (Corresponding angles of […]
Read More →A diagonal of a parallelogram, divides it into two congruent triangles. Given: A parallelogram ABCD and AC is a diagonal, the diagonal AC divides parallelogram ABCD into two triangles △ ABC and △ CDA. To prove: These triangles △ ABD and △CDA are congruent, △ ABC ≅ △ CDA Proof: In △ ABC and △ CDA BC ∥ AD and AC […]
Read More →If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Given: ABCD is a quadrilateral, each pair of opposite sides of quadrilateral ABCD are AB and CD and also sides AD and BC are equal. AB = CD BC = AD To prove: ABCD is a parallelogram. Construction: Join A to C that is AC, is […]
Read More →In a parallelogram opposite sides are equal. Given: A parallelogram ABCD, each pair of Opposite sides of parallelogram are side AB and side DC and side AD and side BC. To prove: Opposite sides of parallelogram are equal that is AB = DC and AD = BC Construction: Join A to C that is AC, is a diagonal, the diagonal AC […]
Read More →If two Lines are parallel to a third line then the lines are parallel to each other. Given: It is given that three lines l, m, and n, and line l ∥ line m and line m ∥ line n. To Prove: Line l ∥ Line n Proof: Let us draw a line p transversal for lines l, m, and n. For lines l […]
Read More →Angle Formed By Two Lines and a Transversal In above figure line l, intersects two lines m and n at the point p and q respectively. Therefore, line l is a “Transversal” for lines m and n. Four angles are formed at the points p, by line l, name of these angles as ∠1, ∠2, ∠3, and ∠4. Four angles are formed […]
Read More →Transversal A “transversal” is a line or line segment, that intersects two or more lines or line segments. In above figure, line x and line y are transversal. In figure line l, intersects lines m and n at the point p and q […]
Read More →If the diagonals of a Quadrilateral, bisect each other then that Quadrilateral is a Parallelogram Given: ABCD is a quadrilateral with AC and BD are diagonals and diagonals intersect each other at O. i.e. OA = OC and OB = OD To Prove: ABCD is a parallelogram. Proof: In △AOD and △COB […]
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