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Examples of Larger Constructions

You’re going to construct a triangle ABC and a quadrilateral ABCD with the following specifications:

1.
A is 60°, the line AB is 5cm long, and B is 90°. Construct the triangle ABC.

What kind of triangle is this? How large is C?

2.
The area of the triangle ABC in Exercise 1 is half the area of the rectangle ABCD.

How long are the sides in the rectangle? How long is the diagonal?

Example 1

ABC

Make an auxiliary figure, which is a small figure of what you’re going to construct. Mark the angles, lengths, and any other information.

Begin the construction:

Example 2

ABCD

Continue the construction by constructing the quadrilateral ABCD:

  • Construct a normal on the line BC in C.

  • Construct a normal on AB in A. Name the intersection between the two normals D. You have now constructed the rectangle ABCD.

  • Because the rectangle is made up of two 30°-60°-90°” triangles, the hypotenuse is twice the length of the shortest leg. That means the diagonal is 2 5cm = 10cm.

  • To find the height of the triangle, you use the Pythagorean theorem: a2 + b2 = c2 BC2 + 52 = 102 BC2 + 25 = 100 BC = 75 BC2 = 75 BC = 8.67cm

    You’ve found that the sides are 5cm and 8.67cm, and the diagonal is 10cm.

Description of construction of a rectangle

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Construction of Larger Figures