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Geogebra Activity
Angle and Diagonal Properties of Kites
Review:
What is a kite?
Sketching:
1. Make two points at (3,0) and (3,5).
2. Connect a segment between the two points.
3. Make two additional points at (1,4) and (5,4). Connect a segment between
these two points as well.
4. Make the following segments: BC, BD, AC, and AD.
5. Lastly, make point E the intersection of AB and CD.
Angle Measurements
1. Find the measure of angle ACB and angle BDA. What is the measure of each
angle?
a. Angle ACB = _______
Angle BDA = _______
b. Click the Move tool and move point B up and down (not passing point
E) vertically.
c. What similarities do you see between angle ACB and angle BDA?
d. Move point B back to its original point at (3,5).
2. Find the measure of angle BEC, angle DEB, angle CEA and angle AED.
a. Move point B up and down vertically again.
b. What similarities do you notice between these angles?
c. Once again, move point B back to its original point at (3,5).
Side Lengths
1. Measure the lengths of segments: BC, BD, AC, and AD. Record them below.
a. BC=
b. BD=
c. AC=
d. AD=
e. CE=
f. DE=
2. How do these side lengths relate to each other?
3. Now, using the Move tool, move the outer points, C and D, to the points (2,3)
and (4,3) respectively. What are the lengths of the sides and what differences
do you notice?
Connections:
1. From measuring the angles and sides, what kind of properties have you
observed about a kite?
2. What happens if you would drag point B lower than point E? Is the figure still
a kite?
ANSWER KEY
Geogebra Activity
Angle and Diagonal Properties of Kites
Review:
What is a kite?
Referring back to prior knowledge, students may have answers
such as: a quadrilateral, a polygon, a shape having two pairs of equal-length sides,
they also may remember that the longer diagonal is a perpendicular bisector of the
shorter bisector
Sketching:
6. Make two points at (3,0) and (3,5).
7. Connect a segment between the two points.
8. Make two additional points at (1,4) and (5,4). Connect a segment between
these two points as well.
9. Make the following segments: BC, BD, AC, and AD.
10. Lastly, make point E the intersection of AB and CD.
Angle Measurements
3. Find the measure of angle ACB and angle BDA. What is the measure of each
angle?
a. Angle ACB = __90 degrees__
Angle BDA = __90 degrees_
b. Click the Move tool and move point B up and down (not passing point
E) vertically.
c. What similarities do you see between angle ACB and angle BDA?
They are the same measure of degrees.
d. Move point B back to its original point at (3,5).
4. Find the measure of angle BEC, angle DEB, angle CEA and angle AED.
a. Move point B up and down vertically again.
b. What similarities do you notice between these angles?
They are all 90 degrees.
c. Once again, move point B back to its original point at (3,5).
Side Lengths
4. Measure the lengths of segments: BC, BD, AC, and AD. Record them below.
a. BC= 2.24 cm
b. BD= 2.24 cm
c. AC= 4.47 cm
d. AD= 4.47 cm
e. CE= 2 cm
f. DE= 2 cm
5. How do these side lengths relate to each other?
Segment BC = BD, Segment AC = AD, and segment CE = segment DE
6. Now, using the Move tool, move the outer points, C and D, to the points (2,3)
and (4,3) respectively. What are the lengths of the sides and what differences
do you notice?
BC = BD = 2.24 cm
AC = AD = 3.16 cm
CE = DE = 1 cm
When moving the outer points, the same sides remain equal to each other.
Connections:
3. From measuring the angles and sides, what kind of properties have you
observed about a kite?
Segment BC is congruent to segment BD
Segment AC is congruent to segment AD
Diagonals are perpendicular bisectors
Angle BCA = Angle BDA
4. What happens if you would drag point B lower than point E? Is the figure still
a kite?
It is not still a kite. It becomes sort of a “pushed-in” kite; a dart.