Consider the following coordinates w(1,8), x (7,8), y(4,5), z(1,2) select all methods you could use to prove triangle wyz is congruent to triangle wyx. a)  ruler/protractorb)  distance formula (sss)c)  slope/distance formula (sas)d)  transitive propertye)  vertical angles theoremf)  alternate interior angles theoremg)  corresponding angles theorem

a) Ruler/Protractor  

b) Distance formula (SSS)

c) Slope/distance formula (SAS)

Step-by-step explanation:

a) Since,  With plotting the points in coordinate plane,

We found the measurement of sides

WX = 6 unit, ZY= 3√2 unit WY = 3√2, WZ = 6 unit and XY = 3√2

Thus, WX ≅ WZ, ZY≅XY and WY≅WY

Therefore By SSS postulate of congruence,

Δ WYZ ≅ Δ WYX

Now, With help of Protector,

We can find the angles ZWY, ZYW, XWY and XYW.

And, we found that,  ∠ ZWY≅∠ XWY, and ∠ZYW≅∠XYW

And, WY≅ WY

Therefore, BY ASA postulate of congruence,

Δ WYZ ≅ Δ WYX

b) With help of distance formula,

unit

unit

unit

unit

unit

Thus, WX ≅ WZ, ZY≅XY and WY≅WY

Therefore By SSS postulate of congruence,

Δ WYZ ≅ Δ WYX

c)  With help of Slope formula we found that,

Slop of the line WX is 0. ( Slope formula )

And, Slope of line WZ=

Thus, ∠ZWX=90°

But, ∠YWX=45° ( By the formula of )

⇒∠ZWY=45°

And, By the distance formula, WZ≅WX

∠ZWY≅∠XWY

And, WY≅ WY

Thus, By SAS postulate of congruence,

ΔWYZ≅ΔWYX

Note: with the help of other Options we can not conclude triangle  WYZ is congruent to triangle WYX.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column