Chapter 13.3, Problem 49SPR

To determine

To explain:

The figure that quadrilateral $BDFH$ .

Answer to Problem 49SPR

The figure that quadrilateral $BDFH$ is square.

Explanation of Solution

Given information:

  

A stained glass that contains the points $A,B,C,D,F,G,H,O$ has the following design.

  

The sides of $BDFH$ are chords that are two congruent arc measurements. Hence, the sides of $BDFH$ are congruent. Since each of the angles within $BDFH$ intercepts a semicircle, each of the angles within $BDFH$ must be equal to $90$ degrees.

Therefore, because $BDFH$ has four congruent sides and four $90$ degrees angles, hence $BDFH$ is a square.