Chapter 6.3, Problem 4PSA

a

To determine

To find: is GHJK is plane figure?

Answer to Problem 4PSA

Yes, given figure covers area

Explanation of Solution

Given information:

Two-line segments $\left(\overline{\text{GJ}}\&\overline{\text{KH}}\right)$ bisect each other at point P

Since GHJK

Can cover area only and has two dimensions only

Hence

GHJK is a simple figure

b

To determine

To find: Are GH and KJ are parallel?

Answer to Problem 4PSA

Yes, GH and JK are parallel

Explanation of Solution

Given information:

Two-line segments $\left(\overline{\text{GJ}}\&\overline{\text{KH}}\right)$ bisect each other at point P

Since, figure is plane figure

It contains two dimensions only and

Opposite sides of the given figure are always parallel

Hence,

GH & JK are parallel

c

To determine

To find: Are GH and KJ are congruent?

Answer to Problem 4PSA

Yes, GH and KJ are congruent

Explanation of Solution

Given information:

Two-line segments $\left(\overline{\text{GJ}}\&\overline{\text{KH}}\right)$ bisect each other at point P

Since, GH and KJ are equal

Thus, by definition of congruency,

  $\overline{\text{GH}}\cong \overline{\text{KJ}}$

d

To determine

To find: The plane e and plane f are parallel

Answer to Problem 4PSA

Yes, given planes are parallel

Explanation of Solution

Given information:

Two-line segments $\left(\overline{\text{GJ}}\&\overline{\text{KH}}\right)$ bisect each other at point P

Since $\overline{\text{HJ}}\perp e$ and also $\overline{\text{HJ}}\perp \text{f}$

It is only possible when

  $\overline{\text{JK}}\parallel \text{f}$ and also $\overline{\text{HG}}\parallel e$

Hence, given planes are parallel $$

e

To determine

To find: what is the most descriptive name for GHJK?

Answer to Problem 4PSA

The most descriptive name for the given figure is rectangle

Explanation of Solution

Given information:

Two-line segments $\left(\overline{\text{GJ}}\&\overline{\text{KH}}\right)$ bisect each other at point P

The figure GHJK consists of

Four sides

Opposite sides are parallel

Opposite sides are equal

All angles are right angle

These all properties belong to RECTANGLE

Hence,

The most descriptive name for the given figure is rectangle