Question

determine if l || m based on the information given on the proves the lines are parallel. 5. given the following information, determine which lines, if any, are parallel. state the converse that justifies your given a. ∠10≅∠15 b. m∠14 + m∠18 = 180° c. ∠4≅∠20 ∠3≅∠16 ∠10≅∠12 m∠19 = 180° ∠17

Explanation:

Step1: Recall parallel - line postulates

If corresponding angles are congruent, alternate - interior angles are congruent, or same - side interior angles are supplementary, then the lines are parallel.

Step2: Analyze case a

Given $\angle10\cong\angle15$. If $\angle10$ and $\angle15$ are corresponding angles (assuming a transversal intersects two lines), by the converse of the corresponding - angles postulate, the two lines intersected by the transversal are parallel.

Step3: Analyze case b

Given $m\angle14 + m\angle18=180^{\circ}$. If $\angle14$ and $\angle18$ are same - side interior angles (assuming a transversal intersects two lines), by the converse of the same - side interior angles postulate, the two lines intersected by the transversal are parallel.

Step4: Analyze case c

Given $\angle4\cong\angle20$. If $\angle4$ and $\angle20$ are alternate - interior angles (assuming a transversal intersects two lines), by the converse of the alternate - interior angles postulate, the two lines intersected by the transversal are parallel.

Answer:

a. The two lines intersected by the transversal are parallel by the converse of the corresponding - angles postulate.
b. The two lines intersected by the transversal are parallel by the converse of the same - side interior angles postulate.
c. The two lines intersected by the transversal are parallel by the converse of the alternate - interior angles postulate.