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.

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step-by-step explanation:

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