<span>Decimal: 0.928571</span>
In the diagram below, TUVW is a rectangle. Prove triangle TZW is congruent to triangle UZV.
1 answer:
Answer:
By S.S.S. congruence property; ΔTZW ≅ ΔVZU
Step-by-step explanation:
Given:
TUVW is a rectangle.
To Prove : TZW ≅ UZV
Proof:
Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.
So,
And also TV and WU are the diagonals of the rectangle.
And the diagonals of rectangle bisects each other.
Therefore;
Now In ΔTZW and ΔVZU
TW = UV (from 1)
TZ = ZV (from 2)
WZ = ZU (from 3)
So, by S.S.S. congruence property;
ΔTZW ≅ ΔVZU
Hence proved.
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<span>Decimal: 0.928571</span>
Answer:
If the kid walks for the dotted line, the distance is 36ft.
Now, you can see that this is a triangle rectangle, then we must have that:
x^2 + (x + 6)^2 = 36^2 (the Pythagorean theorem)
Now we must solve this for x.
x^2 + x^2 + 2*6*x + 36 = 36^2
2*x^2 + 12*x -1260 = 0
The solutions for this equation are:
the solutions are:
x = (-12 - 101.1)/4 = -28.78
x = (-12 + 101.1)/4 = 22.3
Then we have x = 22.3 ft
The lenght of the path following the cathetus is:
D = x + x + 6 = 2*22.3ft + 6ft = 50.6ft
Then the difference between the distances is:
Diff = 50.6ft -36ft = 14.6ft