Question

1. △abc is a right triangle definition of a right triangle
2. ba = √(1 + d²)

bc = √(e² + 1)
ca = √((d - e)²) = d - e application of the distance formula

1. (√(1 + d²))² + (√(e² + 1))² =? pythagorean theorem
2. (1 + d²) + (e² + 1) = d² - 2de + e²

2 + d² + e² = d² - 2de + e²
2 = -2de
-1 = de simplify

1. -1 = m_abm_bc substitution property of equality

which expression is missing from step 7?
○ a. (d - e)²
○ b. -2de
○ c. (a + b)²
○ d. a² + b²

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here, \(BA=\sqrt{1 + d^{2}}\), \(BC=\sqrt{e^{2}+1}\) are the legs (assuming \(CA\) is the hypotenuse \(CA = d - e\)).

Step2: Apply Pythagorean theorem formula

By the Pythagorean theorem \((\sqrt{1 + d^{2}})^{2}+(\sqrt{e^{2}+1})^{2}=(d - e)^{2}\)

Answer:

A. \((d - e)^{2}\)