Question

Consider the following coordinates

Answer 1

Answer: 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,

$WX =\sqrt{(7-1)^2+(8-8)^2} = 6$ unit

$ZY= \sqrt{(4-1)^2+(5-2)^2} =3\sqrt{2}$ unit

$WY= \sqrt{(4-1)^2+(5-8)^2} =3\sqrt{2}$ unit

$WZ= \sqrt{(1-1)^2+(2-8)^2} =6$ unit

$XY= \sqrt{(4-7)^2+(5-8)^2} =3\sqrt{2}$ 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 $m=\frac{y_2-y_1}{x_2-x_1}$ )

And, Slope of line WZ= $\infty$

Thus, ∠ZWX=90°

But, ∠YWX=45° ( By the formula of $tan\theta =\frac{m_1-m_2}{1+m_1m_2}$ )

⇒∠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 2

The methods that could be used to prove triangle WYZ is congruent to triangle WYX are:

a) Ruler/Protractor
b) Distance formula (SSS)
c) Slope/distance formula (SAS)