given: $\overline{fe} \perp \overline{gj}$\
$\angle 6 \cong \angle 1$\
prove: $\overline{fg} \perp \overline{kh}$\
step statement reason\
1 $\overline{fe} \perp \overline{gj}$ given\
2 $\angle 6 \cong \angle 1$ given\
3 $\overline{fg} \perp \overline{kh}$ if corr. $\angle$s $\cong$, then lines $\perp$.\
validate this line is incorrect.

Question

Accepted Answer

# Explanation:
## Step1: Analyze FE ⊥ GJ
Since $\overline{FE} \perp \overline{GJ}$, $\angle 6$ and $\angle 5$ are complementary (they form a right angle), so $m\angle 6 + m\angle 5 = 90^\circ$.
## Step2: Use ∠6 ≅ ∠1
Given $\angle 6 \cong \angle 1$, so $m\angle 6 = m\angle 1$ (congruent angles have equal measures).
## Step3: Find relationship of ∠1 and ∠5
Substitute $m\angle 6$ with $m\angle 1$ in $m\angle 6 + m\angle 5 = 90^\circ$, we get $m\angle 1 + m\angle 5 = 90^\circ$. This means $\angle 1$ and $\angle 5$ are complementary, so $\overline{FG} \perp \overline{KH}$ (if two angles forming a linear pair with a transversal are complementary, the lines are perpendicular). The original reason was incorrect as it used parallel line reasoning, but we need perpendicular line reasoning here.
# Answer:
To correct step 3: The statement $\overline{FG} \perp \overline{KH}$ should have the reason "If two angles ( $\angle 1$ and $\angle 5$) formed by a transversal ( $GJ$) with two lines ( $FG$ and $KH$) are complementary, then the lines are perpendicular" (or using the right angle definition: since $m\angle 1 + m\angle 5 = 90^\circ$, $\angle FKH$ (or the angle between $FG$ and $KH$) is $90^\circ$, so they are perpendicular).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Analyze FE ⊥ GJ

Step2: Use ∠6 ≅ ∠1

Step3: Find relationship of ∠1 and ∠5

Answer: