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,
[tex]WX =\sqrt{(7-1)^2+(8-8)^2} = 6[/tex] unit
[tex]ZY= \sqrt{(4-1)^2+(5-2)^2} =3\sqrt{2}[/tex] unit
[tex]WY= \sqrt{(4-1)^2+(5-8)^2} =3\sqrt{2}[/tex] unit
[tex]WZ= \sqrt{(1-1)^2+(2-8)^2} =6[/tex] unit
[tex]XY= \sqrt{(4-7)^2+(5-8)^2} =3\sqrt{2}[/tex] 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 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] )
And, Slope of line WZ= [tex]\infty[/tex]
Thus, ∠ZWX=90°
But, ∠YWX=45° ( By the formula of [tex]tan\theta =\frac{m_1-m_2}{1+m_1m_2}[/tex] )
⇒∠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.
