Geometry paragraph proofs?

Question

Use a paragraph proof to prove triangle CAT is congruent to triangle DOG.

Given:
angle A = 10x+2
angle O = 5x+12
angle C = 13x-10
angle D = 2x+12
CT=3x+7 and DG=x+11.

Please help! I'd really appreciate it!

Answer 1

One of the way you can prove that two triangles are congruent is to prove that two of their angles, and the side between them, are congruent, aka the SAS theorem.

So to prove that these triangles are congruent, you can pick any pair of angles or the two sides, and solve for x. Then if that same x works in the other 2 cases, the triangles must be congruent for that value of x.

Assume that the triangles are congruent. I'll start with the sides.

Then CT = DG, so 3x + 7 = x + 11.

3x + 7 = x + 11
2x = 4
x = 2

So CT 3(2) + 7 = 13 and DG = 2 + 11 = 13.

If the triangles are really congruent, then x = 2 should work in the angles too.

10(2) + 2 = 22, and 5(2) + 12 = 22, so the measure of angle A equals the measure of angle O.

13(2) - 10 = 16, and 2(2) + 12 = 16, so the measure of angle C equals the measure of angle D.

So since we have SAS when x = 2, the triangles are congruent if and only if x = 2.

(Notice however that it is important to say "if and only if x = 2", because of x has any other value, the triangles are NOT congruent.)

Answer 2

A paragraph evidence is somewhat like a 2-column evidence different than in paragraph variety. you employ finished sentences; it extremely is like what you're able to tell somebody else. here is an occasion: Triangle ABC is congruent to Triangle DEF via ASA. so which you placed each and every fact and reason in one sentence.