Question

HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP!!!!

2. ⦁ Justify each step in solving the equation by writing a reason for each statement.
3. ⦁ Provide reasons for the proof.
PLEASE ANSWER CORRECTLY, THE PICTURES ARE BELOW

Answer 1

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]