In figure if AB \(\parallel \) CD .EF \(\bot \) CD and \(\angle \) AGE,\(\angle \) GEF and \(\angle \) FGE

3

(a)

Prove that bisectors of pair of vertically opposite angles are in the same straight line.

3

(a)

In the figure, if x+y=w+z, then prove that AOB is a straight line.

3

(a)

In the given figure, l||m||n. From the figure, find the ratio of (x+y):(y-x).

3

(a)

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

3

(a)

In the figure, l||m. Prove that \(\angle 1+\angle2-\angle3=180^o\)

3

(a)

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

3

(a)

In figure, a transversal l cuts two lines AB and CD at E and F respectively. EG is the bisector of \(\angle AEF\) and FH is the bisector of \(\angle EFD\) such that \(\angle a=\angle b.\) Show that EG||FH and AB||CD.

3

(a)

In figure, triangle ABC is right angles at A, AL is drawn perpendicular ro BC. Prove that \(\angle BAL=\angle ACB.\)

3

(a)

In the given figure, if \(\angle BCD=25^0,\angle BAQ=110^o\ and\ \angle ACR=125^o\), then find the values of x, y, z.

3

(a)

In the given figure \(\angle 3\) and \(\angle 4\) are exterior angles of quadrilateral ABCD at point D and B respectively. and \(\angle A=\angle 2, \angle C=\angle 1.\) Prove that \(\angle 3+\angle 4=\angle1+\angle2\)

3

(a)

In the given figure, find the value of x^o

3

(a)