G.CO.13 ASSESSMENT – PATTERSON 1 MULTIPLE CHOICE 1. Given the diagram, determine the description which is false. A) The circle is inscribed in the square. B) The triangle is inscribed in the circle. D) The circle circumscribes the triangle. C) The square is inscribed in the circle. 2. Given the diagram, determine the description which is false. A) The circle circumscribes the hexagon. B) The hexagon circumscribes the triangle. C) The hexagon is inscribed in the circle. D) The triangle is inscribed in the circle. Answers: 1. C 2. D TRUE/FALSE 1. A circle circumscribes an equilateral triangle, then the circle is in the interior of the equilateral. T or F Answers: 1. F G.CO.13 ASSESSMENT – PATTERSON 2 SHORT ANSWER 1. A student is constructing an equilateral triangle inscribed in a circle. They got to this point of the construction and realized that a smaller equilateral was hidden in the diagram, ΔABC. Why would this be an equilateral triangle? Answer: AB = AC (congruent radii of circle A) and CA = CB (congruent radii of circle C) AB = AC = CB (transitive) Three congruent sides is an equilateral triangle. A
B
C
2. A student is constructing a hexagon inscribed in a circle. They got to this point of the construction and realized there were six hidden equilaterals in the hexagon. Name the six equilateral triangles and explain why they are equilateral triangles? Answer: ΔBAG, ΔGAE, ΔEAC, ΔCAD, ΔDAF, ΔFAB All segments in these triangles are congruent radii. B
G
A
E
F
D
C
3. Circle the correct relationship. a) Relationship between the circle and the triangle: The triangle is inscribed / circumscribed b) Relationship between the circle and square: c) Relationship between the square and the triangle: The square is inscribed / circumscribed The triangle is inscribed / circumscribed Answers: a) Inscribed b) Circumscribed c) Inscribed 4. Circle the correct relationship. A) Relationship between the circle and the triangle: The triangle is inscribed / circumscribed / Neither B) Relationship between the circle and the rectangle: The circle is inscribed / circumscribed / Neither C) Relationship between the hexagon and the rectangle: The rectangle is inscribed / circumscribed / Neither Answers: a) Circumscribed b) Neither c) Inscribed G.CO.13 ASSESSMENT – PATTERSON 5. What is the next step in constructing an inscribed equilateral triangle? 3 B
A
C
Answer: To create a circle with the same radius as circle A but centered at either B or C. LONG ANSWER 1. Draw the following relationships. a) A square inscribed in a circle b) A triangle circumscribed about a circle c) A hexagon inscribed in a circle Answer: G.CO.13 ASSESSMENT – PATTERSON 2. Construct an inscribed hexagon. 4 Answer: B
B
B
A
E
G
B
A
E
A
F
A
A
E
B
E
C
D
C
D
F
C
D
3. Construct an inscribed square. Answer: B
B
B
B
A
A
A
A
E
E
E
C
D
D
D
A
C
C
C
4. Construct an inscribed equilateral triangle. Answer: B
B
A
B
A
E
E
B
A
A
A
D
C
C
G
F
C
D
G
D
E
C
D
C