Discovering Properties of Kites

The applet below contains a quadrilateral that ALWAYS remains a kite. The purpose of this applet is to help you understand many of the geometric properties a kite has. Some of these properties are unique and only hold true for a kite (and not just any quadrilateral). The questions you need to answer are displayed below this applet.

Use the features within this GeoGebra applet to investigate the answers to the following questions:

1) Are OPPOSITE SIDES of a kite congruent?[br]

Yes No

[size=150] If so, how many pairs?[/size]

No pairs of OPPOSITE sides are congruent. 3 pair 4 pair 1 pair 2 pair

2) Are ADJACENT SIDES of a kite congruent?

Yes No

[size=150] If so, how many pairs?[/size]

3 pair No pairs of ADJACENT sides are congruent. 2 pair 4 pair 1 pair

3) Are any pairs of OPPOSITE angles of a kite congruent?

Yes No

[size=150] If so, how many pairs?[/size]

No pairs of OPPOSITE angles are congruent. 3 pair 1 pair 2 pair 4 pair

4) Are any pairs of ADJACENT angles of a kite congruent?

No Yes

[size=150] If so, how many pairs?[/size]

No pairs of ADJACENT angles are congruent. 3 pair 4 pair 1 pair 2 pair

5) Are the diagonals of a kite congruent?

No Yes

6) Do the diagonals of a kite bisect EACH OTHER?

No Yes

7) Does either diagonal of a kite get bisected by the other diagonal?

No Yes

If so, which diagonal gets bisected?

[math]BC[/math] [math]DA[/math] [math]CD[/math] [math]BD[/math] [math]AB[/math] [math]AC[/math]

8) Does any diagonal of a kite bisect a pair of opposite angles?

One diagonal bisects a pair of opposite angles. Both diagonals bisect a pair of opposite angles. Neither diagonal bisects a pair of opposite angles.

If so, which diagonal(s)?

[math]AC[/math] bisects [math]\angle BAD[/math] and [math]\angle BCD[/math] [math]BD[/math] bisects [math]\angle ABC[/math] and [math]\angle ABD[/math] [math]BD[/math] bisects [math]\angle ABC[/math] and [math]\angle ABD[/math][br]AND[br][math]AC[/math] bisects [math]\angle BAD[/math] and [math]\angle BCD[/math] Neither diagonal bisects a pair of opposite angles.

9) Are the diagonals of a kite perpendicular?

No Yes

What do you observe about the triangles created by the diagonals?

Discovering Properties of Kites

Use the features within this GeoGebra applet to investigate the answers to the following questions:

Information: Discovering Properties of Kites