Question

kayla wants to prove the pythagorean theorem: if a triangle is a right triangle, then the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

triangle abc with right angle at b

select the appropriate rephrased statement for kaylas proof.
choose 1 answer:
a) in △abc, if ∠b = 90°, then ab² = bc² + ac².
b) in △abc, if ab² = bc² + ac², then ∠b = 90°.
c) in △abc, if ∠b = 90°, then ab² + bc² = ac².
d) in △abc, if ab² + bc² = ac², then ∠b = 90°.

Explanation:

The Pythagorean theorem states that in a right - triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In $\triangle ABC$, $\angle B = 90^{\circ}$, so the hypotenuse is $AC$. The other two sides are $AB$ and $BC$. So according to the theorem, $AB^{2}+BC^{2}=AC^{2}$.

• Option A: The formula is wrong as it should be $AB^{2}+BC^{2}=AC^{2}$ not $AB^{2}=BC^{2}+AC^{2}$.
• Option B: This is the converse of the Pythagorean theorem (it states that if $AB^{2}=BC^{2}+AC^{2}$, then $\angle B = 90^{\circ}$), but Kayla wants to prove the original theorem, not the converse.
• Option D: This is also the converse of the Pythagorean theorem.

Answer:

C. In $\triangle ABC$, if $\angle B = 90^{\circ}$, then $AB^{2}+BC^{2}=AC^{2}$.