Question

1. if lines $overline{ab}$ and $overline{cd}$ are parallel to each other, we would show that in symbols by using which of the following? (1) $overline{ab}congoverline{cd}$ (2) $overline{ab}paralleloverline{cd}$ (3) $overline{ab}=overline{cd}$ (4) $overline{ab}perpoverline{cd}$
2. how many points in common will two parallel lines contain? (1) 1 (2) 2 (3) 0 (4) an infinite number of points
3. in trapezoid $efgh$, $overline{ef}perpoverline{he}$, $overline{he}perpoverline{hg}$, and $overline{ef}paralleloverline{hg}$. which two sides, if extended forever, would not intersect? (1) $overline{ef}$ and $overline{hg}$ (2) $overline{ef}$ and $overline{fg}$ (3) $overline{he}$ and $overline{fg}$ (4) $overline{he}$ and $overline{ef}$
4. in the diagram below, lines $h$ and $i$ are crossed by transversal $k$. which two angles represent an alternate interior angle pair? (1) $angle2$ and $angle4$ (2) $angle1$ and $angle4$ (3) $angle4$ and $angle5$ (4) $angle3$ and $angle6$
5. according to the parallel - line postulate, if point $a$ does not lie on line $n$, then which of the following is the number of unique lines that can be drawn through point $a$ parallel to line $n$? (1) 1 (2) 2 (3) an infinite number of lines (4) 0

n - gen math geometry - unit 1 - beginning concepts - lesson 9

Explanation:

Step1: Recall parallel - line symbol

The symbol for parallel lines is $\parallel$. So, if lines $\overline{AB}$ and $\overline{CD}$ are parallel, we write $\overline{AB}\parallel\overline{CD}$.

Step2: Recall properties of parallel lines

Parallel lines are lines in a plane that do not intersect. So, they have 0 points in common.

Step3: Analyze trapezoid sides

In trapezoid $EFGH$ with $\overline{EF}\parallel\overline{HG}$, if extended forever, $\overline{EF}$ and $\overline{HG}$ will not intersect.

Step4: Identify alternate - interior angles

Alternate - interior angles are on opposite sides of the transversal and between the two lines. For lines $h$ and $i$ crossed by transversal $k$, $\angle3$ and $\angle6$ are alternate - interior angles.

Step5: Apply parallel - line postulate

According to the Parallel Line Postulate, if a point $A$ does not lie on line $n$, then exactly 1 unique line can be drawn through point $A$ parallel to line $n$.

Answer:

1. (2) $\overline{AB}\parallel\overline{CD}$
2. (3) 0
3. (1) $\overline{EF}$ and $\overline{HG}$
4. (4) $\angle3$ and $\angle6$
5. (1) 1