Lesson 2: Problem Solving - Drawing Similar Polygons Example 2


EXAMPLE 2

Draw a figure similar to the one shown that is a reduction (smaller) by factor of 1.5.



Solution


Step 1: Label the vertices.



Step 2: Measure each angle and side length. Record your findings.

To make measuring the angles easier, measure and record the acute angles (the angles smaller than 90°) and the right angles (90°), rather than the reflex angle.

Angles Original Side Length
∠A = 45° AB = 12 cm
∠B = 45° BC = 7.5 cm
∠C = 90° CD = 7.5 cm
∠D = 45° DE = 12 cm
∠E = 45° EF = 7.5 cm
∠F = 90° AF = 7.5 cm

Step 3: Multiply or divide each of the side lengths by the given scale factor.

The question states that the polygon should be smaller by a factor of 1.5. This means to divide each side length by 1.5.

Angles Original Side Length New side length
∠A = 45° AB = 12 cm AB′= 8 cm
∠B = 45° BC = 7.5 cm BC′= 5 cm
∠C = 90° CD = 7.5 cm CD′= 5 cm
∠D = 45° DE = 12 cm DE′= 8 cm
∠E = 45° EF = 7.5 cm EF′= 5 cm
∠F = 90° AF = 7.5 cm FA′= 5 cm

Step 4: Draw one of the sides with its new measure.

This example starts with side AB, but you can start with any of the sides.



Step 5: Measure the angle at one end of the new side, and make a small mark (the angles do not change in a scale drawing).

In this example, angle B (45°) is drawn, but angle A could be drawn as well. Remember that the angle measures do not change.



Step 6: Draw the next side, going through the small angle mark. This side length should correspond to the calculated length in step 3.

Line segment BC is drawn next, with a length of 5 cm.



Note, sometimes the mark for the angle is outside (beyond) the side length. Be sure to have the ruler lined up with the angle mark before drawing the side length needed.

Step 7: Repeat steps 5 and 6 until all sides are drawn.

i) marking ∠C (90°)

ii) line segment CD drawn 5 cm in length

iii) marking ∠D (45°)

iv) line segment DE at 8 cm in length

v) marking ∠E (45°)

vi) line segment EF 5 cm in length

vii) connect the last side with one last line, then verify in step 8.


Step 8: Measure the last side and measure the angle between the first and last sides.

The last side (AF) measures 5 cm.
Angle F measures 90°

Here are the original figure and the reduction.




Now, it is your turn! Complete the questions in your Chapter 8, Lesson 2 Practice Makes Perfect that refer to Drawing Similar Polygons 2.



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