In δabc (m∠c = 90°), the points d and e are the points where the angle bisectors of ∠a and ∠b intersect respectively sides bc and ac . point g ∈ ab so that dg ⊥ ab and h ∈ ab so that eh ⊥ ab . prove that δceh and δcdg are isosceles.

Proof: and are isosceles triangles.

Explanation: Given in D and E are angle bisector of   and respectively.

Where G and H are points in AB such that and .

Let us take two triangles and

(Right angles)

BE=BE, (common segment)

( Because BE is angle bisector)

Thus, (ASA)

Therefore, EH= CE (CPCT)

So, in , EH=CE ⇒ is an isosceles triangle.

Now, in and ,

(Right angles)

AD=AD (common segment)

( Because AD is angle bisector)

⇒ (ASA)

Thus, CD=DG (CPCT)

So, in , CD=DG ⇒ is an isosceles triangle.

the answer

b. they are parallel and will never intersect.