Question

complete the proof that $overleftrightarrow{rt} perp overleftrightarrow{su}$. 1. $angle rvscongangle svt$ 2. $mangle rvs + mangle svt=180^{circ}$ 3. $mangle rvs + mangle rvs = 180^{circ}$ 4. $mangle rvs = 90^{circ}$ 5. $overleftrightarrow{rt} perp overleftrightarrow{su}$

Explanation:

Step1: Given angle - congruence

$\angle RVS\cong\angle SVT$ (Given)

Step2: Linear - pair property

$m\angle RVS + m\angle SVT=180^{\circ}$ (Angles forming a linear pair sum to $180^{\circ}$)

Step3: Substitution

Since $\angle RVS\cong\angle SVT$, we substitute $m\angle SVT$ with $m\angle RVS$: $m\angle RVS + m\angle RVS = 180^{\circ}$

Step4: Solve for $m\angle RVS$

Combining like - terms gives $2m\angle RVS=180^{\circ}$, then $m\angle RVS = 90^{\circ}$ (Divide both sides by 2)

Step5: Definition of perpendicular lines

Since $m\angle RVS = 90^{\circ}$, by the definition of perpendicular lines, $\overleftrightarrow{RT}\perp\overleftrightarrow{SU}$

Answer:

1. Given
2. Angles forming a linear pair sum to $180^{\circ}$
3. Substitution
4. Simplification (divide both sides of $2m\angle RVS = 180^{\circ}$ by 2)
5. Definition of perpendicular lines