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Circles

Question

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I. m and n are three parallel lines intersected by transversals p and q such that I, m and n cut off equal intercepts AB and BC on p (see figure). Show that l, m and n cut off equal intercepts DE and EF on q also.

Solution

Solution not provided.

Some More Questions From Circles Chapter

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD respectively (see figure). Show that:
(i) ∆APB ≅ ∆CQD
(ii) AP = CQ.

In ∆ABC and ∆DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, Band C are joined to vertices D, E and F respectively (see figure). Show that:
(i) quadrilateral ABED is a parallelogram
(ii) quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) quadrilateral ACFD is a parallelogram

(v) AC = DF
(vi) ∆ABC ≅ ∆DEF. [CBSE 2012

ABCD is a trapezium in which AB || CD and AD = BC (see figure): Show that
(i) ∠A = ∠B
(ii)    ∠C = ∠D
(iii)    ∆ABC = ∆BAD
(iv)    diagonal AC = diagonal BD.

[Hint. Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.

If a diagonal of a parallelogram bisects one of the angles of the parallelogram, it also bisects the second angle and then the two diagonals are perpendicular to each other.

“A diagonal of a parallelogram divides it into two congruent triangles.” Prove it.

Show that the diagonals of a square are equal and perpendicular to each other.

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