Question

1. draw the vertical line segment ac
2. ∠abc is a right angle
3. △abc is a right triangle
4. ba = √(1 + d²)

bc = √(e² + 1)
ca = √((d - e)²)=d - e

1. (√(1 + d²))²+(√(e² + 1))²=?

(1 + d²)+(e² + 1)
2 + d² + e²

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

-2de

1. -1 = mabmbc

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

Explanation:

Step1: Expand \((d - e)^2\)

By the formula \((a - b)^2=a^{2}-2ab + b^{2}\), when \(a = d\) and \(b=e\), we have \((d - e)^2=d^{2}-2de+e^{2}\).

Step2: Analyze the simplification process

In step 8, we start from \(2 + d^{2}+e^{2}-1\) and simplify it to \(d^{2}-2de + e^{2}\). The missing step 7 should be the expansion of \((d - e)^2\) which gives us the form \(d^{2}-2de+e^{2}\).

Answer:

D. \((d - e)^2\)