Name: Date: Period: Lab: Inscribed Quadrilaterals

Transcription

1 Name: Date: Period: Materials: ompass Straightedge Lab: Inscribed Quadrilaterals Part A: Below are different categories of quadrilaterals. Each category has 2-4 figures. Using a compass and straightedge, determine whether or not each quadrilateral can be inscribed into a circle. If the center of the quadrilateral is not already provided, construct the diagonals to find it. (Note: If the diagonals do not intersect in the center of the shape, you might need to find the midpoint of one diagonal.) Parallelogram: Rectangle:

2 Rhombus: Square: Trapezoid: Note: The center of the circle is in each diagram below.

3 Kite: Part B: Answer the following questions based on your constructions and using the Properties of Inscribed Quadrilaterals. 1. an a parallelogram always, sometimes, or never be inscribed into a circle? Explain. 2. an a rectangle always, sometimes, or never be inscribed into a circle? Explain. 3. an a rhombus always, sometimes, or never be inscribed into a circle? Explain. 4. an a square always, sometimes, or never be inscribed into a circle? Explain. 5. an a trapezoid always, sometimes, or never be inscribed into a circle? Explain. 6. an a kite always, sometimes, or never be inscribed into a circle? Explain.

4 Name: _ANSWER KEY Date: Period: Materials: ompass Straightedge Lab: Inscribed Quadrilaterals Part A: Below are different categories of quadrilaterals. Each category has 2-4 figures. Using a compass and straightedge, determine whether or not each quadrilateral can be inscribed into a circle. If the center of the quadrilateral is not already provided, construct the diagonals to find it. (Note: If the diagonals do not intersect in the center of the shape, you might need to find the midpoint of one diagonal.) Parallelogram: Rectangle:

5 Rhombus: Square: Trapezoid: Note: The center of the circle is in each diagram below.

6 Kite: Part B: Answer the following questions based on your constructions and using the Properties of Inscribed Quadrilaterals and the characteristics of each quadrilateral. 1. an a parallelogram always, sometimes, or never be inscribed into a circle? Explain. Sometimes. The parallelogram would have to be a rectangle or a square because the opposite angles are both congruent and supplementary (right angles). Having the opposite angles being supplementary is required to create the circle. 2. an a rectangle always, sometimes, or never be inscribed into a circle? Explain. Always. The opposite angles are both congruent and supplementary (right angles). Having the opposite angles being supplementary is required to create the circle. Also the diagonals are congruent and bisect each other, which makes the radius of the circle. 3. an a rhombus always, sometimes, or never be inscribed into a circle? Explain. Sometimes. The rhombus would have to be a square because the opposite angles are both congruent and supplementary (right angles). Having the opposite angles being supplementary is required to create the circle. 4. an a square always, sometimes, or never be inscribed into a circle? Explain. Always. The opposite angles are both congruent and supplementary (right angles). Having the opposite angles being supplementary is required to create the circle. Also the diagonals are congruent and bisect each other, which makes the radius of the circle. 5. an a trapezoid always, sometimes, or never be inscribed into a circle? Explain. Sometimes. The trapezoid would have to be isosceles because the opposite angles are both supplementary. Having the opposite angles being supplementary is required to create the circle. 6. an a kite always, sometimes, or never be inscribed into a circle? Explain. Sometimes. The kite would have the congruent angles be right angles in order for this to work because only = 180, and the opposite angles have to be supplementary in order for the quadrilateral to be inscribed in a circle.