Question

1. given the points l, m, n and o located at l(0, - 2), m(5,8), n(-1,5), and o(7,3) do the following (a) plot and label all four points. (b) draw $overline{lm}$ and $overline{no}$. (c) find the intersection point of $overline{lm}$ and $overline{no}$. label it as point p on the diagram. state the coordinates of p below. (3,4) (d) $angle mpn$ and $angle lpo$ are what type of angle pair? (e) what does (d) tell you about the measures of $angle mpn$ and $angle lpo$?

Explanation:

Step1: Recall angle - pair types

Vertical angles are formed when two lines intersect. They are opposite each other.

Step2: Identify the angle - pair

Since $\angle MPN$ and $\angle LPO$ are formed by the intersection of $\overline{LM}$ and $\overline{NO}$ and are opposite each other, they are vertical angles.

Step3: Recall the property of vertical angles

Vertical angles are congruent, which means they have equal measures.

Answer:

(d) Vertical angles
(e) The measures of $\angle MPN$ and $\angle LPO$ are equal.