Chapter 1.2, Problem 4PSA

a.

To determine

To Find: The missing terms.

Answer to Problem 4PSA

  $\overrightarrow{QV}\cap \overleftrightarrow{TS}=T$

Explanation of Solution

Given:

  

  $\overrightarrow{QV}\cap \overrightarrow{TS}=\_?\_\_$

Concept Used:

Intersections of a ray and a line are the points common between them.

Since a ray moves in one direction which have one initial point but no terminal point.

Calculation:

Here, the ray QV meets the line TS in T, hence

  $\overrightarrow{QV}\cap \overleftrightarrow{TS}=T$

Conclusion:

  $\therefore \overrightarrow{QV}\cap \overleftrightarrow{TS}=T$

b.

To determine

To Find: The missing terms.

Answer to Problem 4PSA

  $\overline{WP}\cap \overline{VR}=\overline{VW}$

Explanation of Solution

Given:

  

  $\overline{WP}\cap \overline{VR}=\_?\_\_$

Concept Used:

Intersections of two line segments are the portion of the line segments common between them.

Calculation:

Here, the intersections of two line segments WP and VR is a line segment VW

  $\therefore \overline{WP}\cap \overline{VR}=\overline{VW}$

Conclusion:

  $\overline{WP}\cap \overline{VR}=\overline{VW}$

c.

To determine

To Find: The missing terms.

Answer to Problem 4PSA

  $\overrightarrow{WP}\cup \overrightarrow{VR}=\overleftrightarrow{VW}$

Explanation of Solution

Given:

  

  $\overrightarrow{WP}\cup \overrightarrow{VR}=\_?\_\_\_$

Concept Used:

Union of two different rays with different initial points is a line.

Calculation:

Here, the rays WP and VR and coinciding with each other, thus we get a line with their union.

  $\overrightarrow{WP}\cup \overrightarrow{VR}=\overleftrightarrow{VW}$

Conclusion:

  $\therefore \overrightarrow{WP}\cup \overrightarrow{VR}=\overleftrightarrow{VW}$

d.

To determine

To Find: The missing terms.

Answer to Problem 4PSA

  $\overrightarrow{SQ}\cup \overrightarrow{SR}=\angle QSR$

Explanation of Solution

Given:

  

  $\overrightarrow{SQ}\cup \overrightarrow{SR}=\_?\_\_\_$

Concept Used:

Union of two different rays with common initial points is a angle.

Calculation:

Here, the rays SQ and SR are passing through a common initial point, thus we get an angle with their union.

  $\overrightarrow{SQ}\cup \overrightarrow{SR}=\angle QSR$

Conclusion:

  $\therefore \overrightarrow{SQ}\cup \overrightarrow{SR}=\angle QSR$

e.

To determine

To Find: The number of angles the vertex Q have.

Answer to Problem 4PSA

Six angles formed at the vertex Q.

Explanation of Solution

Given:

  

Concept Used:

A angle is formed when two different rays passes through the same point, i.e., rays having same initial point.

Calculation:

Here, the rays QR, QW, QS, QV, QT and QP are passing through a common initial point Q, thus we get different angles using the vertex Q. Thus, the angle formed at the vertex Q are

  $\angle SQR,\angle TQS,\angle PQT,\angle PQS,\angle TQR\text{and }\angle PQR$ .

Thus six angles formed at the vertex Q.

Conclusion:

Six angles formed at the vertex Q.