Chapter 6.5, Problem 3CYP

(a)

To determine

To find: Whether she can conclude that each yellow piece is a rhombus.

Answer to Problem 3CYP

It cannot conclude that each yellow pieces is a rhombus.

Explanation of Solution

Given Information:

The given figure is

  

It is given that she marks a diagonals of each yellow pieces and determines each pair is perpendicular to each other’s.

But it cannot conclude that each yellow pieces are rhombus. There can be other options like square and rectangle.

Hence, it cannot conclude that each yellow pieces is a rhombus.

(b)

To determine

To find: Whether she can conclude that each green piece is a square.

Answer to Problem 3CYP

It is a square.

Explanation of Solution

Given Information:

The given figure is

  

It is given that all four angles of the green pieces have the same measure and the bottom and the left sides have the same measure.

Thus, the remaining sides are also equal.

Since the diagonal is perpendicular to each other thus, its all four angles are also $90°$ .

Hence, it is a square.