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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.