• Chinook High School

• MATH III

M 3.7.4 Test (TST):Constructions and Transformations Test

(4 Geometry Points Possible: Sem 2 50 Name: Date Zoe Tng

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 Poseiblc A

Bisecting a segment with a

perpendicular segment @oSsible

Doubling a cube oSS ble

Doubling a square pessiple

Drawing an equilateral triangle pose ble

Drawing a regular hexagon posSI ble

Tripling a square Po5St ble

Trisecting a right angle pPOSS ble

Trisecting a segment Poss, b

Trisecting any given angle ipossiow

2. The rules for constructions are based on the flve basic postulates of Euclldean 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.

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C. Third postulate: A circle can be drawn with any center and radius

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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.

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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.

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Jeanne's idea the shape

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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)

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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)

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vaoli d4heah ke first one

Step 3: Describe the final steps in constructing the shape of the earring. Include a drawing.

(2 points)

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