A triangle is a simple geometric shape. All triangles are closed and flat. They have three straight edges and three corners. There are lot of variations to how triangles may be drawn. Here are some images of triangles that differ in shape.
Regularities to triangles are identified as their geometric properties. Each type of geometric shape has specific geometric properties that always hold. These are like rules of geometry.
Example 1 below makes use of two geometric properties of triangles to solve a geometry problem. Here are the two properties mentioned in bold.
Sum of all three angles of a triangle is 180°.
In a triangle with two of three edges (or sides) equal in length (called an isosceles triangle), the angles opposites to the two sides are also equal.
Find the unknown angles x and y in the triangle below. The given triangle is isosceles whose two non-base sides are equal.
Since the two non-base sides are equal, the angles opposite to them are also equal
x = 70
Sum of all three angles in a triangle is 180°
y + 70 + 70 = 180
y + 140 = 180
y = 180 – 140
y = 40
So angle x is 70° and angle y is 40°.
Example 2 is an application of Pythagoras Theorem. This theorem describes an exact relationship among lengths of all three sides of a right-angled triangle. It does not apply to other triangles. A right-angled triangle has one angle of 90° also called a right angle. The relationship which is a property of all right-angled triangles is described below in bold.
Square of the length of the longest side of a right-angled triangle (which is opposite to the largest angle of 90°) equals the sum of the squares of the lengths of the other two sides.
Find the unknown side in the right-angled triangle below
Using Pythagoras Theorem
5² = x² + 4²
25 = x² + 16
x² = 25 − 16
x² = 9
√x² = √9
x = 3
The length of unknown side is 3 units.
Many people find study of shapes an interesting fun. There can be lot of variety and variations to them. They are visual and thinking about them involves imagination. They may be drawn on paper. Models of them may be built and then actually seen and studied closely.
Basic-Mathematics is a website that provides excellent information about basic geometry. Here is a link to the first geometry article on the site