Trapezoidal Stone Arch

Scenario: Trapezoidal Stone Arch Instructions: View the video found on page 1 of this Journal activity. Using the information provided in the video, answer the questions below.

Show your work for all calculations.

The Students’ Conjectures: During an archeological dig, the students found a voussoir from a semicircular stone arch. A voussoir is a trapezoidal (wedge-shaped) stone used to build an arch or vault.

1. What are the students trying to find out? (1 point)

2. Complete the table to summarize each student’s conjecture: (2 points: 1 point for each row)

3. Draw a picture that shows the trapezoidal stone and the information that you know: (1 point)

4. Is this is an isosceles trapezoid? How do you know? (1 point)Understand the problem: Measuring an existing arch.

Consider Serena’s picture of an arch that is still standing. It has 9 voussoirs (or trapezoidal stones). What are the angles for each trapezoid?

5. Draw the interior triangles that go to the base center of the arch: (1 point)

6. Calculate the small angle for each interior triangle: (2 points)

7. Calculate the base angles for each interior triangle: (2 points)

8. Find the angles of the trapezoid: (2 points: 1 point for each pair of angles)

Solving the problem: How many stones were in the original arch? Work the same scenario backwards, starting with the stone.

9. Find the interior angles of the trapezoid that the students found: (2 points: 1 point for each angle base pair)

10. Draw the isosceles triangle that would extend to the center of the arch. Find the angles of that triangle. (2 points)

11. Given that the entire arch forms a semicircle, how many stones are in the arch? (2 points)

Evaluate the Conjecture: 12. Who was correct? Is there more than one way to build an arch out of trapezoidal stones? If so, why? (2 points)

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