Constructing an Angle of 90 degrees
The construction of an angle of 90 degrees can be done in two ways - by using a compass and by using a protractor. Making a rough sketch is different from that of construction in geometry. In geometry, by construction, we mean drawing shapes, lines, angles with more accurate measurements. The pieces of equipment that we would need are a ruler, compass, and a protractor. Construction in geometry always starts with a point. We then extend to draw a line segment or a line and from there on constructing the required shape or angle. An angle in geometry is the space between two lines that intersect each other. 90° denotes a right angle in geometry. Sometimes, there is a need to construct angles without using a protractor. Let us learn how to construct an angle of 90 degrees in this article.
| 1. | Construction of 90° Angle Using Compass |
| 2. | Construction of 90° Angle With Protractor |
| 3. | Solved Examples |
| 4. | Practice Questions |
| 5. | FAQs on Constructing an Angle of 90° |
Construction of 90° Angle Using Compass
In this section, you will learn how to construct a 90 degrees angle with the help of a compass. The steps to construct an angle of 90 degrees are as follows.
Step 1: Draw a line segment of any length and label its endpoints as A and B.
Step 2: Using the compass and with any width as radius and with A as a center, draw an arc that cuts the line segment AB at a point and label it as C.
Step 3: With the same radius and with point C as the center, draw an arc that cuts the previous arc and name it as D.
Step 4: With D as a center and with the same radius draw another arc and name it as E.
Step 5: With the same radius and with D and E as center draw two arcs that cut each other and label it as F.
Step 6: Now join the points F and A. Now we can observe that ∠FAB = 90°.
Construction of 90° Angle With Protractor
Constructing an angle of 90° can also be done using a protractor. A protractor is a geometric instrument that has markings of angles on it. Let us look into the steps to do the same.
Step 1: Draw a line segment XY of any measurement.
Step 2: Place the midpoint or center of the protractor on point X.
Step 3: Starting from 0° in the protractor, move in the anti-clockwise direction and mark a point in the place of 90° as Z.
Step 4: Join the points Z and X. Now, ∠ZXY measures 90°.
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Solved Examples
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Example 1: Construct a perpendicular bisector for a line segment of length AB = 8 units and check if the angle formed by the perpendicular bisector with the line segment is 90° or not.
Solution:
Step 1: Draw a line segment with length AB = 8 units.
Step 2: With A as the center, and more than half the length of AB as radius, draw an arc on both the sides of the line segment AB. Repeat the same process with B as center and the same radius. Mark the points of intersection as P and Q.
Step 3: Join the points P and Q. PQ is the perpendicular bisector of AB. Also, we can observe that the perpendicular bisector makes an angle of 90° with the line segment AB.
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Example 2: What are some real-life examples where we can observe 90°?
Solution:
The angles formed by the arms of the windmill, the clock showing nine o'clock, and the angle formed at the corners of rectangular windows and doors are some of the real-life examples where we can observe 90°.
FAQs on Constructing an Angle of 90 Degrees
What is an Angle of 90° Called?
An angle of 90° is called a right angle. Constructing an angle of 90° can be done by measuring 90° in the protractor or by constructing a perpendicular bisector to a straight line. The perpendicular bisector makes 90° with a straight line.
How Do You Construct an Angle of 90° With a Compass and a Ruler?
To construct an angle of 90° with a compass and a ruler, follow the steps mentioned below:
- Draw a line and label its endpoints as A and B.
- Using the compass with any width as radius and with A as a center, draw an arc that cuts the line segment AB at a point and label it as C.
- With the same radius and with point C as the center, draw an arc that cuts the first arc and name it as D.
- With D as a center and with the same radius draw another arc and name it as E.
- With the same radius and with D and E as center draw two arcs that cut each other and label it as F.
- Now join the lines F and A. Now we can observe that angle FAB = 90°.
How Do You Construct an Angle of 90° With a Protractor and a Ruler?
To construct an angle of 90° with a protractor and a ruler, follow the steps mentioned below:
- Draw a line segment and label it as XY.
- Place the midpoint or center of the protractor on point X.
- Starting from 0° in the protractor, move in the anti-clockwise direction and mark a point in the place of 90° as Z.
- Join the points Z and X. Now the angle ZXY measures 90°.
What is the Angle Formed by a Perpendicular Bisector?
The angle formed by a perpendicular bisector is 90°. A perpendicular bisector is a line segment that divides a line segment into two parts that are equal and makes an angle of 90°.
How to Construct an Angle of 90° and Bisect It?
Draw a line segment AB. Place the protractor on point A and measure 90° and label it as C. Join CA. Now, with A as center draw an arc on CA and AB and mark it as E and F. With E and F as center draw two arcs that cut each other and label it as G. Now, join G and A. The line segment GA bisects 90° and forms two angles each of 45 degrees.