**Geometry Distance of Triangles using a Protractor**

Eileen Lally A. Philip Randolph Magnet School

7316 South Hoyne Avenue

Chicago IL 60636

(773) 535-9015

**Objectives**:

Students in the 7th grade are to learn how to use the protractor to measure

angles, and use this ability to solve a problem involving distance.

**Materials Needed**:

Protractors for each student

Rulers and meter sticks

Straws and clay

**Strategy**:

PART ONE

1. Identify the vocabulary: ray, angle, vertex, unit of measure,

protractor

2. Demonstrate or review how to use the protractor.

3. Draw a 60cm line labeled AB on the board. Instruct students to draw a 6cm

line labeled ab on paper.

4. At point A/a make a 35^{o} and at point B/b make a 60^{o}. Make sure that the rays

are extended until they cross. Label that point C.

5. Compare the triangles (the one on the board and the one on paper).

These triangles are similar.

6. Present the question: What is the distance of the line segment AC without

leaving your desk?

7. Set up the ratio: line AB over line ab = X (AC) over line ac.

8. Now measure the line AC and compare the result with the calculated answer.

Use the formula: Actual measurement minus Calculated measurement

divided by Actual to obtain the margin of error.

PART TWO

1. Upon a large table, mark two points A and B and determine the distance

(AB) between them.

2. Use the protractor to determine the measure of angle BAC. Likewise,

determine the measure of angle ABC.

3. We now attempt to determine X, the distance (AC) from the point A to the

Point C. Make a model (as described in Part 1) keeping the angles found but

reduce the size of line segment ab. Set up the ratio: Line AB over line ab

= X (AC) over line ac.

4. To verify, measure the distance from point A to point C. Compare with the

calculated answer. Use the formula: Actual measurement minus Calculated

measurement divided by Actual to obtain the margin of error.

**Performance Assessment**:

A similar problem like part two can be used as a performance assessment.

The students are to answer the following question. What is the length of

line AC?

**Conclusion**:

Knowing two angles and the distance between them, you can find the distance

of the point that completes the triangle. This can be done by making a

smaller model to help calculate the answer.

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