Question

rt || fh and fh || uw. complete the proof that m∠qvu + m∠rsx = 180°. statement reason 1 rt || fh 2 fh || uw 3 ∠qvu ≅ ∠fgq 4 m∠fgq + m∠rsx = 180° 5 m∠qvu + m∠rsx = 180°

Explanation:

Step1: Given information

Given that $\overleftrightarrow{RT}\parallel\overleftrightarrow{FH}$ and $\overleftrightarrow{FH}\parallel\overleftrightarrow{UW}$

Step2: Corresponding - angles postulate

Since $\overleftrightarrow{UW}\parallel\overleftrightarrow{FH}$, $\angle QVU$ and $\angle FGQ$ are corresponding angles, so $\angle QVU\cong\angle FGQ$ (Corresponding - angles postulate: If two parallel lines are cut by a transversal, then the corresponding angles are congruent)

Step3: Same - side exterior angles theorem

Since $\overleftrightarrow{RT}\parallel\overleftrightarrow{FH}$, $\angle FGQ$ and $\angle RSX$ are same - side exterior angles. So $m\angle FGQ + m\angle RSX=180^{\circ}$ (Same - side exterior angles theorem: If two parallel lines are cut by a transversal, then the sum of the measures of two same - side exterior angles is $180^{\circ}$)

Step4: Substitution property

Since $\angle QVU\cong\angle FGQ$, then $m\angle QVU = m\angle FGQ$. Substituting $m\angle QVU$ for $m\angle FGQ$ in the equation $m\angle FGQ + m\angle RSX = 180^{\circ}$, we get $m\angle QVU + m\angle RSX=180^{\circ}$

Answer:

1. Given
2. Given
3. Corresponding - angles postulate
4. Same - side exterior angles theorem
5. Substitution property