State whether segments of the given lengths can be side of a right angle triangle. a=7, b=24, and C=25.
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2 Points

Given:

In a triangle,

To find:

Whether the given segments are the sides of a right triangle or not.

Solution:

In a right triangle the square of largest side is equal to the sum of squares of two smaller side.

                (Pythagoras theorem)

Three sides are . Here, 25 is the largest side.

Now, the sum of squares of two smaller sides is:

Since the sum of squares of two smaller side is equal to the square of largest side, therefore the given segments are the sides of a right triangle.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

c. 1,233 miles