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Chapter 2: Problem 13

Construct a right isosceles triangle with legs that are about 2 inches in length.

Short Answer

Expert verified
Draw two perpendicular legs of 2 inches each and connect their ends.

Step by step solution

01

Draw the First Leg

Use a ruler to draw a straight horizontal line that is exactly 2 inches long. This will be the first leg of the right isosceles triangle.
02

Draw the Second Leg

From one end of the first leg, draw another straight line that is exactly 2 inches long and perpendicular to the first leg. Use a protractor to ensure the angle is 90 degrees.
03

Connect the Hypotenuse

Finally, connect the free ends of the two legs with a straight line. This line is the hypotenuse of the right isosceles triangle.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

triangle construction
Constructing a triangle involves a series of steps to ensure accuracy. In this activity, we will focus on constructing a right isosceles triangle. This type of triangle can be easily constructed by understanding simple geometric principles and using basic tools like a ruler and a protractor. The following steps will help you in constructing your desired triangle:
  • First, identify the length of the legs you aim to draw. In this example, the legs are 2 inches each.
  • Second, ensure your tools are properly calibrated. A good ruler and a precise protractor are crucial.
  • Third, take your time and draw carefully to maintain precision.
These basic steps lay the foundation for constructing any triangle accurately.
right angle
A right angle is an angle that measures exactly 90 degrees. It is fundamental in geometry and is represented by a small square at the vertex of the angle. Creating a right angle in our triangle is critical for it to be right isosceles:
  • Use a protractor to measure and draw a 90-degree angle accurately.
  • Start by placing the protractor's midpoint at the point where you'd like the two legs of the triangle to meet.
  • Ensure the baseline of the protractor aligns with the drawn line, and carefully mark the 90-degree point.
By maintaining accuracy here, a perfect right isosceles triangle can be achieved.
isosceles triangle
An isosceles triangle is one that has at least two sides of equal length. For a right isosceles triangle, these two equal sides form the right angle. The defining properties make the construction straightforward:
  • Draw two legs of equal length.
  • Ensure these legs meet at exactly a 90-degree angle.
  • The hypotenuse will automatically balance the triangle, connecting the ends of the legs.
Understanding these properties will help visualize and draw the triangle more effectively.

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Most popular questions from this chapter

Construct a right triangle with legs about 2 inches and 3 inches in length, respectively.

Draw a scalene acute triangle and construct its three angle bisectors. Label the incenter.

Will the centroid of a triangle always be inside the triangle? Explain.

Draw a scalene obtuse triangle and construct its three medians. Label the centroid.

Write a two-column or flowchart proof. [ Note: For the remainder of the book, the key will only show a two-column proof. This is done for efficiency.] (Angle can't copy) \(\begin{aligned} \text {Given:} & \overrightarrow{A C} \text { bisects } \angle B A D \\ & \overrightarrow{C A} \text { bisects } \angle B C D \end{aligned}\) Prove: \(\angle B \cong \angle D\)
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