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MATH 613— VG COMPETENCY PRACTICE Geometry and Measurement: K - 8 Learning and Teacher Practices Be sure to use correct geometrical language and references, see the reading for correct form. 1. Classify each curve as i) simple, ii) simple closed, iii) closed, or iv) none of these. a. b. c. d. e. 2. Classify each region as i) convex or ii) concave. a. b. c. d. e. 3. Sketch an example of each of the following figures. a. Concave pentagon b. Concave decagon c. A simple curve that is not closed d. Convex pentagon e. Convex decagon 4. For this question, angle refers to interior angle. a. Which angles, if any, are acute? b. Which angles, if any, are obtuse? c. Which angles, if any, are right angles? d. Which angles, if any, are reflex angles? 5. Determine whether the following statements about triangles are true or false. For each false statement show a counterexample or explain why the statement is false. a. An equilateral triangle is always an isosceles triangle b. Some triangles have two obtuse angles. c. A triangle cannot be both right and isosceles. 6. Determine whether the following statements about triangles are true or false. For each false statement show a counterexample or explain why the statement is false. a. An isosceles triangle can have three different angles b. A triangle cannot be both right and scalene. c. A scalene triangle can have three congruent angles 7. Determine whether the following statements about quadrilaterals are true or false. For each false statement show a counterexample or explain why the statement is false. a. A rhombus can be a rectangle. b. Every parallelogram is a rectangle. c. An isosceles trapezoid can be a kite. MATH 613— VG COMPETENCY PRACTICE Geometry and Measurement: K - 8 Learning and Teacher Practices 8. Determine whether the following statements about polygons are true or false. For each false statement show a counterexample or explain why the statement is false. a. A circle is a polygon. b. All triangles are convex. c. A polygon cannot have a reflux angle. 9. Draw some figures to determine whether the following statements are true or false. For each false statement show a counterexample. a. If the two diagonals in a parallelogram have the same length, the parallelogram is a rectangle. b. If the midpoints of the adjacent sides of a rectangle are connected, another rectangle is formed. c. If the midpoints of the adjacent sides of a quadrilateral are connected, a parallelogram is formed. 10. Determine whether the following statements about polygons are true or false. a. All parallelograms are convex b. A circle is a polygon c. A regular pentagon with the interior diagonals drawn in to make a star is a polygon. Answers