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Lines and Angles - Bisecting

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Now, we are going to look at another topic under lines and angles, bisecting. The meaning of this can be derived from the name itself. 'Bi' means 2 and bisecting means dividing something exactly in half, like this orange here, But In this lesson. we will only look at line and angle bisecting.  You might think that we could bisect a line just by marking the midpoint and drawing a line through it. But this is not quite so simple. If you draw a line like that, It might not be straight or exactly perpendicular to the original line. So it can't be taken as a bisector.  To correctly bisect a line, we need a compass. We open the compass wider than half of the given line and place it one one end of the line. Then we draw an arc on both sides of the line. We do the same thing after placing compass on the other end of the line. Now we have to arcs on either side of the line. It will appear like this, Then we just have to plot points at the intersecting points of the arcs and join the
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Lines and Angles - Constructing shapes

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lines and angles are heard of in almost every topic under mathematics. The relationship between these and the many different creations it can make are both complex and beautiful. From these, the first we'll be looking into is the construction of shapes using these lines and angles.  There are quite a lot we can do under this too but lets stick to your syllabus right? When we are constructing rectangles and triangles, one thing to always remember is that all the angles in both is 90 degrees. So the important thing to consider here is the length of the sides. To draw a square, knowing just one side length is enough. For example, we are asked to construct a square of with a side length of 5 cm. To do this we start by drawing one side of the square. Then we take 90 degrees from one end of that line with a protractor. Like so, Then mark the 90 degrees degrees point with a pencil.  Note: Remember to start count from the scale starting with 0 at the line. The protractor provides a scale i
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Trigonometry

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Trigonometry is a concept which shows the relationship between the sides and angles in a right angled triangle. This helps us to find unknown sides and angles when we have limited information. But to before we get into this, we need to learn how to label the sides of a triangle in trigonometry. The side opposite to the right angle (the longest side of the triangle) is called the hypotenuse,  How the other 2 sides are labelled depends on the angle we choose (other than the right-angle). the side opposite to the angle chosen is called 'opposite' and the remaining angle is called 'adjacent'.  Here, the angle opposite to the angle in blue, which we are considering as the angle we need, is labelled 'opposite' and the remaining angle 'adjacent'. However, should the angle needed change, these 2 labels also change.  Now that we know how to label, lets look at the relationship between these. There are 3 formulas that defines this for us which can be quite easily
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Pythagoras Theorem

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Developed by a Greek mathematician, Pythagoras of Samos, Pythagoras theorem is not just some triangles and their sides drawn on a piece of paper. It is a universal principal that can be seen in everything we see and do. For example, taking a shortcut in a road, construction,  and even in our shadow. Pythagoras theorem shows the relationship between 3 sides of a right angled triangle. To understand this, lets first look at how be label the sides.  The side opposite to the right angle in a triangle or what you might recognize more as the longest side of a right angled triangle is called the hypotenuse.   After identifying the hypotenuse, the other 2 sides can be labelled a and b. The order doesn't matter. Now for the sake of writing down an equation, were going to represent hypotenuse as c. The exact relation between these 3 is that square of 'a' plus square of 'b' will be equal to square of 'c'. Hence, we derive the following equation from this information: T
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