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.

54

step-by-step explanation:

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !