If a +b =1 and a-b = 7, find the values of : 1) 5(a^2 +b^2) ii) ab

1) 5(a^2+b^2) = 125

2) ab = -12

Step-by-step explanation:

a + b = 1

a = 1 - b --(1)

a - b = 7 --(2)

sub (1) into (2):

1 - b - b = 7

-2b = 6

b = -3

when b = -3, a = 4

therefore,

1) 5(a^2+b^2) = 5(4^2 + (-3)^2) = 5(25) = 125

2) ab = 4(-3) = -12

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

          Statement                                     Reason

1.   GH ║ KJ                                      Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ     Alternate interior angle theorem

3. GH ≅ KJ                                        Definition of parallelogram

4.  Δ GLH ≅ Δ JLK                            ASA postulate of congruence

Hence, proved...