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If you take some lines and join them such that the end point of the first line meets the starting point of the last line, you will get a polygon . Each line that makes up the polygon is known as a side . A polygon has interior angles. These are the angles that are inside the polygon. The number of sides of a polygon equals the number of interior angles. If a polygon has equal length sides and equal interior angles, then the polygon is called a regular polygon . Some examples of polygons are shown in [link] .
A triangle is a three-sided polygon. There are four types of triangles: equilateral, isosceles, right-angled and scalene. The properties of these triangles are summarised in [link] .
Name | Diagram | Properties |
equilateral | All three sides are equal in length (denoted by the short lines drawn through all the sides of equal length) and all three angles are equal. | |
isosceles | Two sides are equal in length. The angles opposite the equal sides are equal. | |
right-angled | This triangle has one right angle. The side opposite this angle is called the hypotenuse . | |
scalene (non-syllabus) | All sides and angles are different. |
If the corners of a triangle are denoted A, B and C - then we talk about $\u25b5ABC$ .
Label | Description | Diagram |
RHS | If the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and the respective side of another triangle, then the triangles are congruent. | |
SSS | If three sides of a triangle are equal in length to the same sides of another triangle, then the two triangles are congruent | |
SAS | If two sides and the included angle of one triangle are equal to the same two sides and included angle of another triangle, then the two triangles are congruent. | |
AAS | If one side and two angles of one triangle are equal to the same one side and two angles of another triangle, then the two triangles are congruent. |
Description | Diagram |
If all three pairs of corresponding angles of two triangles are equal, then the triangles are similar. | |
If all pairs of corresponding sides of two triangles are in proportion, then the triangles are similar. | $\frac{x}{p}=\frac{y}{q}=\frac{z}{r}$ |
If $\u25b5$ ABC is right-angled ( $\widehat{B}={90}^{\circ}$ ) then ${b}^{2}={a}^{2}+{c}^{2}$
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