Home
Class 9
MATHS
Two parallel lines l and m are inters...

Two parallel lines l and m are intersected by a transversal p (see Fig. 8.15). Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

Text Solution

Verified by Experts

`angle AEF+angle BEF=180^(@)` (linear pair)
`rArr (1)/(2) (angle AEF) +(1)/(2)(angle BEF)=90^(@)`
`rArr angle GEF + angle FEH=90^(@) rArr angle GEH=90^(@).`
Now, `angle AEF + angle CFE = 180^(@)" "("co-interior " angle )`
`rArr (1)/(2) (angle AEF)+(1)/(2) (angle CFE)=90^(@)`
`rArr angle GEF + angle GFE=90^(@) rArr angle EGF=90^(@)`
`("sum of " angle " of a " triangle " is " 180^(@)).`
Similarly, `angle GFH= angle EHF=90^(@).`
Promotional Banner

Similar Questions

Explore conceptually related problems

Two parallel lines 1 and m are intersected by a transversal p (see Fig.8.15) .Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Two parallel lines AB and CD are intersected by a transversal line EF at M and N, respectively. If the lines MP and NP are the bisectors of the interior angles BMN and DNM on the same side of the transversal, then angleMPN is equal to

If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of interior angles enclose a rectangle.

If two parallel lines are intersected by a transversal , then the interior angles on the same side of the transversal are -

If two parallel lines intersected by a transversal; prove that the bisectors of the two pairs of interior angle encloses a rectangle.