(Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions.

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1 Seventh Grade Mathematics Assessments page 1 (Geometry) Academic Standard: TLW use appropriate tools to perform basic geometric constructions. A. TLW use tools to draw squares, rectangles, triangles and parallelograms with given dimensions. Directions: Use appropriate tools to draw the polygons according to the dimensions given below. Appropriate tools include a ruler and protractor. 1. Draw a square with a side of 3 cm. 2. Draw a rectangle with a length of 6 cm and a width of 4 cm. 3. Draw a triangle whose sides are 7 cm, 6 cm, and 3 cm.

2 Seventh Grade Mathematics Assessments page 2 4. Draw a triangle with sides of 5 cm and 8 cm that have an included angle of 40º. 5. Draw a parallelogram with sides 4 cm and 9 cm that have an included angle of 65º. Criteria: Reasonably accurate and neat drawings; adherence to Geometric Constructions Checklist on page 9

3 Seventh Grade Mathematics Assessments page 3 B. TLW copy a segment and construct a perpendicular bisector of a segment. Directions: Copy AB onto line l. Label the congruent segment CD and then construct the perpendicular bisector of CD. Label the bisector EF. Leave your construction marks showing. Use only a pencil, compass and straightedge as your tools for the construction. B A l Criteria: Reasonably accurate copy, construction, and label; adherence to Geometric

4 Seventh Grade Mathematics Assessments page 4 C. TLW copy an angle and construct an angle bisector. Directions: Follow the instructions for each drawing. 1. Copy ABC using B'A' with the vertex of the congruent angle at point B'. Label the congruent angle A'B'C' and then construct the angle bisector of A'B'C'. Label the bisector B'D. Leave your construction marks showing. Use only a pencil, compass and straight edge as your tools for the construction. A A' C B B' 2. Copy EFG using F'E' with the vertex of the congruent angle at point F'. Label the congruent angle E'F'G' and then construct the angle bisector of E'F'G'. Label the bisector F'H. Leave your construction marks showing. Use only a pencil, compass and straight edge as your tools for the construction. E F E' F' G Criteria: Reasonably accurate copies, constructions, and labels; adherence to Geometric

5 Seventh Grade Mathematics Assessments page 5 D. TLW construct a line perpendicular to a given line from a point on the line and construct a line perpendicular to a given line from a point not on the line. Directions: Do the following construction. Leave your construction marks showing. Use only a pencil, compass and straightedge as your tools for the construction. 1. Given point I on PT, construct the perpendicular to the line through point I. Label the perpendicular line IK. P J T 2. Given point A above MN, construct the perpendicular to MN through point A. Label the perpendicular line. Criteria: Reasonably accurate constructions and labels; adherence to Geometric

6 Seventh Grade Mathematics Assessments page 6 E. TLW construct a line parallel to a given line through a point not on the line. Directions: Construct the parallel to line MN through point A. Label the parallel line. Leave your construction marks showing. Use only a pencil, compass and straight edge as your tools for the construction. A N M Criteria: Reasonably accurate constructions and labels; adherence to Geometric

7 Seventh Grade Mathematics Assessments page 7 F. TLW construct a triangle given the sides. Directions: Do the following constructions. Leave your construction marks showing. Use only a pencil, compass and straight edge as your tools for the construction. 1. Given the following three sides of a triangle, construct the triangle and label the vertices. 2. Given one side of an equilateral triangle, construct the triangle and label the vertices. Criteria: Reasonably accurate constructions and labels; adherence to Geometric

8 Seventh Grade Mathematics Assessments page 8 G. TLW make geometric constructions involving two or more single-step constructions. Directions: Show all construction marks. 1. Develop a method to construct a segment three times as long as XY. Show your construction on the given line and explain your method. X Y Explanation: 2. Construct a square using a compass and straight edge and using ST as one side. Construct the midpoint of each side. Connect consecutive midpoints and explain what you think is special about the new figure. S T Explanation: Criteria: Neatness, accuracy and evidence of appropriate construction marks; adherence to Geometric

9 Seventh Grade Mathematics Assessments page 9 Follows directions (draw, copy, and/or construct). Uses tools appropriately. Shows all construction marks when required. Geometry Constructions Checklist Labels appropriately as required in diagram. Gives mathematically correct and complete explanations (informal justifications), when required. Yes No

10 Seventh Grade Mathematics Assessments page 10 (Answer Key) A Adherence to Geometric. Check drawings with ruler and protractor to determine accuracy. B Adherence to Geometric. Construction should follow directions. See Resource 7:9a for sample response. C Adherence to Geometric. Construction should follow directions. See Resource 7:9b for sample response. D. 1. Adherence to Geometric. Construction should follow directions. See Resource 7:9c for sample response. 2. Adherence to Geometric. Construction should follow directions. See Resource 7:9d for sample response. E. 1. Adherence to Geometric. Construction should follow directions. See Resource 7:9e for sample response. F. 1. Adherence to Geometric. Construction should follow directions. See Resource 7:9f for sample response. G. Adherence to Geometric Constructions Checklist Sample responses: 1. Set the compass for the distance XY. Place the compass at the point M and draw a construction mark intersecting MT. Repeat #2 using the intersection on MT. Repeat again. Conclusion: From M to the 3 rd construction mark is 3 times XY. 2. Construct the perpendicular bisector of CL. Label W as the midpoint of CL. Setting the compass to the distance CW, make construction marks from the corners on the sides and label X, Y, and Z respectively. Connect the midpoints (W, X, Y, Z). Conclusion: WXYZ is a square that is equal to 1 the area of the square CDML. 2 D Y M X Z C W L

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