Arrange the sentences of the paragraph proof in the most logical order. Given: GH has a length of 16 cm.
Prove: If point 7 is the midpoint of GĦ, then GT = 8 cm.
1. If point 7 is the midpoint of GH, then GT= TH by the definition of midpoint.
2. Assume that I is the midpoint of GH and that GT+8 cm. Let GT= 5 cm.
3. GH= GT+TH by the segment addition postulate. Therefore, GH= 5 cm + 5 cm = 10 cm. GH= 10 cm and GH = 16 cm,
which is a contradiction.
4. If GT= 8 cm, then a contradiction occurs. Therefore, the original statement is true by proof by contradiction.
A 1, 2, 3, 4
B. 2, 1, 3,4
C. 2, 4, 1,3
D. 4, 3, 1, 2

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

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus