Chapter 4.4, Problem 20PPS

(a)

To determine

To explain:

The three-dimensional figure represented by the wet floor sign.

Answer to Problem 20PPS

The three-dimensional figure represented by the wet floor sign is triangular pyramid.

Explanation of Solution

Given information:

  

The three-dimensional figure represented by the wet floor sign is triangular pyramid.

(b)

To determine

To prove:

  $\Delta ACB\cong \Delta ACD$

Explanation of Solution

Given information:

  

  $\overline{AB}\cong \overline{AD}$

  $\overline{CB}\cong \overline{DC}$

Proof:

Proof	Reason
$\overline{AB}\cong \overline{AD}$   $\overline{CB}\cong \overline{DC}$	Given.
$\overline{AC}\cong \overline{AC}$	Reflective property.
$\Delta ACB\cong \Delta ACD$	SSS − Side, Side, Side.

(c)

To determine

To explain:

The reason for the triangle is not congruent in the given diagram.

Answer to Problem 20PPS

The object is three-dimensional,so when it is viewed in two dimensions, theperspective makes it look like the triangles aredifferently shaped. Thus, the triangles are not congruent.

Explanation of Solution

Given information:

  

The object is three-dimensional,so when it is viewed in two dimensions, theperspective makes it look like the triangles aredifferently shaped.

Thus, the triangles are not congruent.