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rosijanka [135]
2 years ago
10

Consider the diagram and the paragraph proof below.

Mathematics
2 answers:
jarptica [38.1K]2 years ago
7 0

Answer:

The answer is b

Step-by-step explanation:

Consider the diagram and the paragraph proof below.

Given: Right △ABC as shown where CD is an altitude of the triangle

Prove: a2 + b2 = c2

 Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to point D on side A B to form a right angle. The length of C B is a, the length of A C is b, the length of A B is c, the length of A D is e, the length of D B is f, and the length of C D is h.

Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).

Which is the last sentence of the proof?

Because f + e = 1, a2 + b2 = c2.

Because f + e = c, a2 + b2 = c2.

Because  a2 + b2 = c2, f + e = c.

Because  a2 + b2 = c2, f + e = 1.

Makovka662 [10]2 years ago
4 0

Answer:

I don't know how I can help you but I found this from another person. Hope this helps!

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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

4x + 1 = 3 - 2x

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Add 2x on both sides:                    6x + 1 = 3
  2. Subtract 1 on both sides:                6x = 2
  3. Divide 6 on both sides:                   x = 1/3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    4(1/3) + 1 = 3 - 2(1/3)
  2. Multiply:                        4/3 + 1 = 3 - 2/3
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Here we see that 7/3 does indeed equal 7/3.

∴ x = 1/3 is a solution of the equation.

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