Lines and are parallel in the image below. the image will be used to prove that the sum of the measures of the interior angles of is 180°. which statement would be included in a proof of why ? angles f and h are congruent. angles a and g are congruent. angles a and h are congruent. angles e and c are congruent.

Third choice:

Angles A and H are congruent.

Why? We use the transverses to copy the triangle angles G, G and H to the same point, where we see they add to a straight line, two right angles, 180 degrees.

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4