3.7.4 Test (TS): Constructions and Transformations Test Archis Chinmulgund Geometry Sem 2 (S3990682) Points possible: 50 Date: ____________ Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work. CONSTRUCTIONS 1. A geometric construction is an accurate drawing of shapes, lines, and angles using only a straightedge and compass. Tell if each geometric construction is possible or impossible. (5 points; 0.5 points each) Construction Possible or Impossible? Bisecting an angle Bisecting a segment with a perpendicular segment Doubling a cube Doubling a square Drawing an equilateral triangle Drawing a regular hexagon Tripling a square Trisecting a right angle Trisecting a segment Trisecting any given angle 2. The rules for constructions are based on the five basic postulates of Euclidean geometry. Complete the diagrams to show each postulate. (5 points; 1 point each) A. First postulate: A straight line segment can be drawn between any two points. B. Second postulate: Any straight line segment can be extended indefinitely. C. Third postulate: A circle can be drawn with any center and radius. D. Fourth postulate: All right angles are equal to one another. E. Fifth postulate: Through a given point not on a given line, there is exactly one line parallel to the given line. NON-EUCLIDEAN GEOMETRY 3. Jeanne makes jewelry and has an idea for a new pair of earrings. She wants to make a sketch of her design, but only has a marker, a pencil, two pieces of paper, and a coffee mug. Use these items to construct the shape of the earring Jeanne is envisioning. Step 1: Jeanne traced her coffee mug on her piece of paper. How might she use paper-folding to find the center of the circle? (2 points) Step 2: Show how a second circle should be drawn in order to continue the construction. What can you say about the radii? Explain your work. (4 points) Step 3: Describe the final steps in constructing the shape of the earring. Include a drawing.(2 points) 4. In the list below, determine whether or not each example is a rigid motion. If it is a rigid motion, identify the type of transformation.(6 points) Example Flipping a pancake Deflating an air mattress Moving a clock's minute hand Enlarging a photo Rigid motion? Yes or No If yes, what type of rigid motion? Putting a golf ball Looking in a car's rear view mirror 5. You are assembling pieces of an iron gate to complete a fence. The finished gate will look like the one below. In order to assemble the gate it is important to understand how the pieces are related . Part I: How are pieces 1 and 2 in the archway related? (1 point) Part II: How are the rectangular sections 5 and 6 in the center of the gate related to each other? (1 point) 6. Give examples of symmetry. Part I: The word BOOK has a horizontal line of symmetry when it is written in all capital letters. Write two other words with four or more letters that have a horizontal line of symmetry. (2 points) Part II: The letter Y has a vertical line of symmetry when it is written as a capital letter. Find five other letters that have a vertical line of symmetry. Then draw each letter showing the lines of symmetry. Show your work. (2.5 points) Part III: Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about a point. Find five letters that have rotational symmetry. Draw each letter showing the point of symmetry. (2.5 points) 7. A line of symmetry divides a design so that every point on one side of the line coincides with a point on the other side of it. Determine how many lines of symmetry each figure below has. Then draw all the lines of symmetry. Show your work. Part I: (5 points) Part II: (5 points) TESSELLATIONS 8. Draw and describe tessellations. Part I: A regular tessellation uses only one regular polygon to completely cover a surface with no overlaps or spaces. Draw a regular tessellation in the box below using only equilateral triangles, squares, or regular hexagons. (3 points) Part II: A semi-regular tessellation uses more than one regular polygon to completely cover a surface with no overlaps or spaces. Name the polygons used in each semi-regular tessellation. (4 points; 2 points each) A. B. Copyright 2017 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use . Any unauthorized copying, reuse, or redistribution is prohibited. Apex Learning and the Apex Learning Logo are registered trademarks of Apex Learning Inc