2. ⦁ justify each step in solving the equation by writing a reason for each statement. 3. ⦁ provide reasons for the proof. answer correctly, the pictures are below

1. QS bisects ∠ PQR of Δ PQR.⇒[Given]

2. ∠PQS = 90° [Given]

3.∠PQS =∠RQS ⇒[QS bisects ∠ PQR]

4. .∠PQS +∠RQS =90°  [∴∠PQS = 90°⇒given]

    2∠PQS =90°⇒  [∠PQS =∠RQS ]

   ∠PQS=45°

So,∠PQS =∠RQS =45°

2.∠ 2= ∠ 4 [Given]

⇒∠ 2≅ ∠ 4[ congruency postulate]

∠2  and ∠ 3 are supplementary.⇒°[given]

⇒∠2 + ∠ 3=180° [ By the definition of supplementary](1)

∠1 and ∠4 are supplementary.⇒[∠1 and ∠4 form linear pair.]

⇒∠1 +∠4=180°[By the definition of supplementary](2)

⇒∠2 + ∠ 3 =∠1 +∠4 [both of them are equal to 180, so they are equal to each other.⇒ Two things equal to same thing are equal to each other[Euclid postulate]]

⇒∠4 +∠3=∠1+∠4 [∠2=∠4⇒(given)]

⇒∠3=∠1   [law of cancellation]

⇒∠3≅∠1  [ Congruency property]

no this is a nonlinear negative

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.