Question

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

Answer 1

Answer:

B. $\dfrac{1}{2}ab$

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:$(a + b)^2 = c^2 + 4(\dfrac{1}{2}ab)$

Step 4: $a^2 + 2ab + b^2 = c^2 + 2ab$

Step 5: $a^2 + b^2 = c^2$

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

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