Question

for all of the problems on this quiz, you must show evidence of your thinking. unless the question says “not online,” you must enter your answers on the online form in google classroom. sc 1: i can use terminology and symbols to analyze points, lines, line - segments, rays, angles, and planes. 1a) which list correctly describes four angles that are drawn on this diagram? a) ∠spv,∠vpq,∠tpq,∠vpt b) ∠spv,∠vpq,∠npt,∠qpt c) ∠psv,∠pqv,∠pqt,∠ptv d) ∠psv,∠pqv,∠pqt,∠mpq e) none of these 1b) what are two other correct names for $overleftrightarrow{pq}$ on the diagram above? a) $overleftrightarrow{qn},overleftrightarrow{pn}$ b) $overleftrightarrow{qn},overleftrightarrow{qp}$ c) $overline{qn},overline{pq}$ d) $overleftrightarrow{qp}$, line $n$ e) none of these 1c) which list correctly describes four rays that are drawn on this diagram? a) $overline{ef},overline{gh},overline{fj},overline{hj}$ b) $overrightarrow{ej},overrightarrow{fj},overrightarrow{gj},overrightarrow{hj}$ c) $overrightarrow{je},overrightarrow{jf},overrightarrow{jg},overrightarrow{jh}$ d) answers b and c are both correct e) none of these 1d) which list contains two correct names for the same line - segment on the diagram above? a) $overline{gh},overline{hg}$ b) $overleftrightarrow{gh},overleftrightarrow{hg}$ c) $overline{gh}$, line j d) $overline{hj},overline{gj}$ e) none of these 1e) what is the complete intersection of plane a and plane b? a) $overleftrightarrow{pq}$ b) $overline{mk}$ c) $overleftrightarrow{mk}$ d) line $k$ e) none of these 1f) not online. add one point to this diagram, label it, then use correct symbols to name a linear pair of angles that includes your new point.

Explanation:

Step1: Recall angle - naming rules

An angle is named using three points with the vertex in the middle. In the first diagram, looking at the angles around point \(P\), the correct angles are \(\angle SPV,\angle VPQ,\angle TPQ,\angle VPT\). So for 1a, the answer is A.

Step2: Recall ray - naming rules

A ray is named with its endpoint first. In the second diagram, rays are named with the endpoint first. Rays \(\overrightarrow{EJ},\overrightarrow{FJ},\overrightarrow{GJ},\overrightarrow{HJ}\) and \(\overrightarrow{JE},\overrightarrow{JF},\overrightarrow{JG},\overrightarrow{JH}\) are correct ways to name rays from point \(J\). So for 1c, the answer is D.

Step3: Recall line - naming rules

A line can be named using two points on the line in either direction or by a single lowercase letter. For \(\overleftrightarrow{PQ}\), two other correct names are \(\overleftrightarrow{Qn}\) and \(\overleftrightarrow{QP}\) (since \(n\) is the line that \(\overleftrightarrow{PQ}\) lies on). So for 1b, the answer is B.

Step4: Recall line - segment naming rules

A line - segment has two endpoints and can be named with the two endpoints in either order. For a line - segment, \(\overline{GH}\) and \(\overline{HG}\) represent the same line - segment. So for 1d, the answer is A.

Step5: Recall plane - intersection rules

The intersection of two planes is a line. In the diagram for 1e, the intersection of plane \(A\) and plane \(B\) is line \(k\). So for 1e, the answer is D.

Step6: For 1f

Add a point \(R\) on line \(k\) outside of the intersection region shown. A linear - pair of angles could be \(\angle PMR\) and \(\angle QMR\) (answers may vary depending on the added point).

Answer:

1a. A. \(\angle SPV,\angle VPQ,\angle TPQ,\angle VPT\)
1b. B. \(\overleftrightarrow{Qn},\overleftrightarrow{QP}\)
1c. D. answers B and C are both correct
1d. A. \(\overline{GH},\overline{HG}\)
1e. D. line \(k\)
1f. Add point \(R\) on line \(k\), linear - pair: \(\angle PMR\) and \(\angle QMR\) (answers may vary)