Home
Class 9
MATHS
A transversal cuts two parallel lines PQ...

A transversal cuts two parallel lines PQ and RS at points A and B respectively. The two interior angles at A are bisected and so are the two interior angles at B, the four bisectors form a quadrilateral ACBD. Prove that:
ACBD is a rectangle

Promotional Banner

Topper's Solved these Questions

  • RECTILINEAR FIGURES

    ICSE|Exercise Exercise 14(A)|14 Videos
  • RECTILINEAR FIGURES

    ICSE|Exercise Exercise 14(B) (true/false)|10 Videos
  • RATIONAL AND IRRATIONAL NUMBERS

    ICSE|Exercise EXERCISE 1 (D)|21 Videos
  • SIMULTANEOUS EQUATIONS

    ICSE|Exercise EXERCISE 6 (G)|13 Videos

Similar Questions

Explore conceptually related problems

A transverals cuts two parallel lines at A and B. The two interior angles at A are bisected and so are the two interior angles at B, the four bisectors from a quadrilateral ACBD, prove that ABCD is parallelogram.

Prove that the bisectors of the interior angles of a rectangle form a square.

Sum of co-interior angles between parallel lines is two right angles

In triangle LMN, bisector of interior angles at L and N intersect each other at point A. Prove that : AM bisects angle LMN.

Two parallel lines l and m are intersected by a transversal p . Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

Theorem 6.2 : If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.