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Nina [5.8K]
3 years ago
15

A triangle has side measures of 8, 13, 15. Are these the measures of a RIGHT Triangle?

Mathematics
1 answer:
Andreas93 [3]3 years ago
6 0

Answer:

No.

Step-by-step explanation:

Since we know the side lengths of the triangle, we can figure out whether or not this is a Pythagorean triple.

Pythagorean theorem: a^2 + b^2 = c^2

a and b are both smaller than c.

So,

8^2 = 64.

13^2 = 169.

15^2 = 225.

64 + 169 = 233.

233 is not equal to 225.

Therefore, this is not a right triangle.

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Given the triangle

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with points

P(8,0)

Q(6,2)

R(-2,-4)

And the triangle

P'Q'R'

with points

P'(4,0)

Q'(3,1)

R'(-1,-2)

Part A. Scale factor

Using the vertex

P( 8, 0)

P'(4,0)

the dilatation factor is given by

\frac{4}{8}=\frac{1}{2}

The triangle has a dilatation factor of 1/2

Part B:

P''Q''R'' after using P'Q'R' reflected about the y axis

to make a reflection over the y axis

coordinates (x,y) turn into coordinates (-x,y)

as follows

P^{\prime}(4,0)\rightarrow P^{\prime\prime}(-4,0)Q^{\prime}(3,1)\rightarrow Q^{\prime\prime}(-3,1)R^{\prime}(-1,-2)\rightarrow R^{\prime\prime}(1,-2)

Then triangle P''Q''R'' has coordinates

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Q''(-3,1)

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PQR is congruent to P''Q''R''?

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