Question

1. name a pair of parallel line segments.
2. name a pair of intersecting line segments.
3. how many acute angles are in figure j?

(figure j shows a quadrilateral with vertices l, m, n, o: l connected to m and o; m connected to l and n; n connected to m and o; o connected to n and l)

Explanation:

Question 7

Step1: Recall parallelogram properties

In a parallelogram (Figure J appears to be a parallelogram), opposite sides are parallel. So, \( \overline{LM} \) and \( \overline{ON} \) are opposite sides.

Step2: Identify parallel segments

From the figure, \( \overline{LM} \parallel \overline{ON} \) (or \( \overline{LO} \parallel \overline{MN} \) as another pair).

Step1: Recall intersecting segments

Intersecting segments share a common endpoint. In the figure, \( \overline{LO} \) and \( \overline{LM} \) share endpoint \( L \), so they intersect.

Step2: Identify intersecting pair

\( \overline{LO} \) and \( \overline{LM} \) (or other pairs like \( \overline{LM} \) and \( \overline{MN} \), \( \overline{MN} \) and \( \overline{NO} \), \( \overline{NO} \) and \( \overline{OL} \)) intersect.

Step1: Recall acute angle definition

An acute angle is less than \( 90^\circ \). In a parallelogram, if it's a non - rectangle parallelogram, there are 2 acute angles (and 2 obtuse angles). Looking at Figure J (a parallelogram), we can observe the angles.

Step2: Count acute angles

By visually inspecting the parallelogram, we see that there are 2 angles that are less than \( 90^\circ \) (the angles at \( L \) and \( N \) or at \( O \) and \( M \), depending on the parallelogram's orientation).

Answer:

\( \overline{LM} \) and \( \overline{ON} \) (or \( \overline{LO} \) and \( \overline{MN} \))

Question 8