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When using the given diagram, the following steps prove the Pythagorean theorem. Step 1: Given yellow triangle abc Step 2: Construct 3 triangles congruent to yellow triangle abc. Step 3: (a + b)2 = c2 + 4( 1 2 ab) Step 4: a2 + 2ab + b2 = c2 + 2ab Step 5: a2 + b2 = c2 Which expression in the proof represents the area of each triangle? A) 4( 1 2 ab) B) 1 2 ab C) ab D) 2ab

Respuesta :

Answer:

B. [tex]\dfrac{1}{2}ab[/tex]

Step-by-step explanation:

Given the proof below:

Proof of Pythagorean theorem.

Step 1: Given yellow triangle abc

Step 2: Construct 3 triangles congruent to yellow triangle abc.

Step 3:[tex](a + b)^2 = c^2 + 4(\dfrac{1}{2}ab)[/tex]

Step 4: [tex]a^2 + 2ab + b^2 = c^2 + 2ab[/tex]

Step 5: [tex]a^2 + b^2 = c^2[/tex]

Since Area of a Triangle =[tex]\frac{1}{2}X$Base X Height[/tex]

The expression that represents the area of each triangle is Option B.

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