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2) 90 degrees & 45 degrees

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In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass.

1. Construction of an Angle of 60° by using Compass
(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B. (iii) With B as centre and the same radius as before, draw another arc to cut the previous arc at C.

(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc cutting OA at B.

(iii) With B as centre and the same radius cut the arc at C, then with C as centre and same radius cut the arc at D. Join OD and produce it to E.

(i) Construction an angle ∠AOD = 60° as shown.

(ii) Draw the bisector OE of ∠AOD.

(i) Take any ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at B.

(iii) With B as centre and the same radius, draw an cutting the first arc at C.

(iv) With C as centre and the same radius, cut off an arc cutting again the first arc at D.

(v) With C and D as centre and radius of more than half of CD, draw two arcs cutting each other at E, join OE.

(i) Take a ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.

(iii) With C as centre and the same radius, draw an cutting the first arc at M.

(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.

(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.

(vi) Now with N and M as centres again draw two arcs cutting each other at P.

(vii) Join OP.

(i) After making 90° angle take L and N as centre and draw two arcs cutting each other at S.

(ii) Join SO.

∠DOE = 45°

∠EOA = 45° + 90° = 135°

Now ∠COD = 30°

Therefore, ∠AOD = 120° + 30° = 150°

`

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Construction of Angles by using Compass, Construction of Angles

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In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass. (i) Draw a ray OA. (ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B.

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1.) 60 degrees & 120 degrees

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In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass.

1. Construction of an Angle of 60° by using Compass
(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B. (iii) With B as centre and the same radius as before, draw another arc to cut the previous arc at C.

(i) Draw a ray OA.

(ii) With O as centre and any suitable radius draw an arc cutting OA at B.

(iii) With B as centre and the same radius cut the arc at C, then with C as centre and same radius cut the arc at D. Join OD and produce it to E.

(i) Construction an angle ∠AOD = 60° as shown.

(ii) Draw the bisector OE of ∠AOD.

(i) Take any ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at B.

(iii) With B as centre and the same radius, draw an cutting the first arc at C.

(iv) With C as centre and the same radius, cut off an arc cutting again the first arc at D.

(v) With C and D as centre and radius of more than half of CD, draw two arcs cutting each other at E, join OE.

(i) Take a ray OA.

(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.

(iii) With C as centre and the same radius, draw an cutting the first arc at M.

(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.

(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.

(vi) Now with N and M as centres again draw two arcs cutting each other at P.

(vii) Join OP.

(i) After making 90° angle take L and N as centre and draw two arcs cutting each other at S.

(ii) Join SO.

∠DOE = 45°

∠EOA = 45° + 90° = 135°

Now ∠COD = 30°

Therefore, ∠AOD = 120° + 30° = 150°

`

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Construction of Angles by using Compass, Construction of Angles

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In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass. (i) Draw a ray OA. (ii) With O as centre and any suitable radius draw an arc above OA cutting it at a point B.

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Perpendicular Lines

Let's begin by talking about perpendicular lines. What exactly are they? Perpendicular lines can be defined as lines that intersect each other at 90 degree angles. Where do you see these in real life? Power poles are usually built perpendicular to the ground if the ground is flat and not on a hill. Also the window screens that keep bugs out are made with perpendicular lines. Take a close look at them and you will see tiny little squares and lots of perpendicular lines intersecting each other.

Why would you want to draw perpendicular lines? If you were an architect or an artist and you wanted to draw perpendicular lines to accurately portray something but you didn't have a way to measure angles, you would use geometric construction to draw your lines.

Geometric Construction

Geometric construction is the drawing of lines, shapes, and angles with only a pencil, compass, and straight edge. There are no numbers or any measuring involved at all. This is the method that you will learn in this video lesson. So if you have your own compass and straight edge, go ahead and grab them so you can follow along.

Setting It Up

To start, we are going to draw a line. Somewhere above the line we are going to draw a dot C. This point C is the point through which we are going to draw our perpendicular line.

The Process

Now take your compass and set one point on point C. Set the width of the compass so that the other end extends past your line. Now draw two arcs that intersect the line to the left and right of the point C. Label the intersection to the left point A and label the intersection to the right point B. You now have a line segment AB.

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constructing perpendicular lines in geometry - video & lesson transcript | study.com

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Constructing Perpendicular Lines in Geometry - Video & Lesson Transcript | Study.com

# data[].attributes.attachment_link.description
Let's begin by talking about perpendicular lines. What exactly are they? Perpendicular lines can be defined as lines that intersect each other at 90 degree angles. Where do you see these in real life? Power poles are usually built perpendicular to the ground if the ground is flat and not on a hill.

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INTRODUCTION:

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Drawing Geometry

One of the truly great things about geometry is that it deals with shapes that you can actually see and manipulate. Is it as fun as playing with counting blocks as a kid when you were first learning to count? Probably not. However, it does beat always trying to find the value of x - the pesky thing keeps changing! But in geometry, you get to learn about important things - like how to find the area of a rectangular room or how much paint you'd need to cover a triangular shape on the side of your suitcase. With that practicality also comes the opportunity to draw things out. In this lesson, we're going to focus on how to best use the various tools available to us in geometry to make sure our diagrams are as accurate as possible.

Rulers and Straight Edges

When making diagrams in geometry class, the most basic tools that you'll find yourself using are rulers and straight edges. Often, these are combined in the same tool, but they are useful nonetheless. Chances are that you know how to draw a line using either, but if you don't, simply trace along the edge.

However, I didn't bring rulers up to just mention how to draw a line. Instead, think about how you'd draw two parallel lines. Now things get a little bit more interesting. To draw a parallel line, first draw a line that you want the parallel line relative to. Now, measure two spots above or below that line, making sure that both are either above or below. However, be sure that the two spots are the same distance away. This is the distance that you want the lines to be apart from one another. Now connect the two lines with a new line, drawn with the ruler or straight edge. As a result, you now have two parallel lines. You can repeat this process as needed if you require additional lines parallel to that first segment.

Protractors

What if you need perpendicular lines, or lines drawn at a certain angle? You can't just use a ruler to make those lines. Instead, you'll need a protractor. A protractor is a half-circle instrument used to measure angles. To use a protractor to draw a perpendicular line, put the base line of the protractor across the line that you are trying to draw a perpendicular line relative to. Make sure that it is the base line within the protractor, signaled by a line running along the edge about a half an inch inside the metal or plastic, and not the base of the protractor itself.

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practice making geometric constructions with tools - video & lesson transcript | study.com

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Practice Making Geometric Constructions with Tools - Video & Lesson Transcript | Study.com

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One of the truly great things about geometry is that it deals with shapes that you can actually see and manipulate. Is it as fun as playing with counting blocks as a kid when you were first learning to count? Probably not.