Since `AB||DC` and `AC` is transversal,
`/_BAC=/_DCA`
Since `AD||BC` and `AC` is transversal,
`/_DAC=/_BCA`
Adding the equations,
`/_DAC+/_BAC=/_DCA+/_BCA`
`/_BAD=/_DCB`
...
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.5|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.6|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.3|1 Videos
LINES AND ANGLES
NCERT ENGLISH|Exercise Exercise 6.1|6 Videos
NUMBER SYSTEMS
NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
Similar Questions
Explore conceptually related problems
The vertices of a quad. PMQS are P(0, 0), M(3, 2), Q(7, 7) and S(4, 5). Show that PMQS is a parallelogram. opposite sides are parallel.
Which of the following is not true for a parallelogram ? a) Opposite sides are equal b) Opposite angles are equal c) Opposite angles are bisected by the diagonals d) Diagonals bisect each other
A quadrilateral is a parallelogram if its opposite sides are equal.
Which of the following statements are true (T) and which are false (F)? (i) In a parallelogram, the diagonals are equal. (ii) In a parallelogram, the diagonals bisect each other. (iii) In a parallelogram, the diagonals intersect each other at right angles. (iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. (v) If all the angles of a quadrilateral are equal, it is a parallelogram. (vi) If three sides of a quadrilateral are equal , it is a parallelogram. (vii) If three angles of a quadrilateral are equal, it is a parallelogram. (viii) If all the sides of a quadrilateral are equal it is a parallelogram
If the altitudes from two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.
If the altitudes from two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.
A quadrilateral is parallelogram if its opposite angles are equal.
Complete each of the following statements by means of one of those given in brackets again each: If one pair of opposite sides are equal and parallel, then the figure is ............... (parallelogram, rectangle, trapezium) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is .............. (square, rectangle, trapezium) A line drawn from the mid-point of one side of a triangle .................. another side intersects the third side at its mid-point. (perpendicular to, parallel to, to meet) If one angle of a parallelogram is a right angle, then it is necessarily a .................... (rectangle, square, rhombus) Consecutive angles of parallelogram are ...................... (supplementary, complementary) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily (rectangle, parallelogram, rhombus) if opposite angles of a quadrilateral are equal, then it is necessarily a ................... (parallelogram, rhombus, rectangle) If consecutive sides of a parallelogram are equal, then it is necessarily a ............. (kite, rhombus, square)
Prove that of all parallelograms of which the sides are given, the parallelogram which is rectangle has the greatest area.
Four particles of masses m, 2m, 3m and 4m are arranged at the corners of a parallelogram with each side equal to a and one of the angle between two adjacent sides is 60^(@) . The parallelogram lies in the x-y plane with mass m at the origin and 4 m on the x-axis. The centre of mass of the arrangement will be located at
