Question

28,148 Learners found this answer helpful

tv || fh and fh || qs. complete the proof that m∠srw + m∠puv = 180°. 1. tv || fh given 2. fh || qs given 3. ∠puv ≅ ∠hgp 4. m∠hgp + m∠srw = 180° 5. m∠srw + m∠puv = 180°

Explanation:

Step1: Identify corresponding angles

Since $\overleftrightarrow{TV}\parallel\overleftrightarrow{FH}$, $\angle PUV$ and $\angle HGP$ are corresponding - angles. Corresponding angles formed by parallel lines are congruent. So the reason for $\angle PUV\cong\angle HGP$ is "Corresponding angles postulate".

Step2: Identify same - side interior angles

Since $\overleftrightarrow{FH}\parallel\overleftrightarrow{QS}$, $\angle HGP$ and $\angle SRW$ are same - side interior angles. Same - side interior angles formed by parallel lines are supplementary, so $m\angle HGP + m\angle SRW=180^{\circ}$. The reason is "Same - side interior angles postulate".

Step3: Substitute

We know that $\angle PUV\cong\angle HGP$, which means $m\angle PUV = m\angle HGP$. Substituting $m\angle PUV$ for $m\angle HGP$ in the equation $m\angle HGP + m\angle SRW = 180^{\circ}$, we get $m\angle SRW + m\angle PUV=180^{\circ}$. The reason is "Substitution property of equality".

Answer:

1. Corresponding angles postulate
2. Same - side interior angles postulate
3. Substitution property of equality