Geometry - Triangles
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A triangle is a three- sided figure.
The most important fact students should remember about triangles is that all triangles always add up to 180 degrees!
This is extremely important to know because it allows us to figure out the missing degrees in a triangle. For example, let's assume that we know a triangle has the angle measures of 40° and 80°. Forty and eighty degrees add up to 120°. Since we know that every triangle has 180°, we can determine the missing degrees by subtracting 180° - 120° to get 60°. Therefore the missing angle is 60 degrees.
There are several different types of angles. Isosceles triangles have two equal angles and opposite those two equal angles it has two equal sides. Equilateral triangles have three equal sides and angles. Scalene triangles have no equal parts.
Another type of triangle, a right triangle, is quite different from the others. A right triangle has a right angle. The two sides of the triangle that form the sides of the right angle are called the legs. The side of the triangle that is opposite the right angle is called the hypotenuse. We can recognize right angles by the little square that sits in the vertex of one of the angles.
When we have the measurements of two sides of a right triangle, we can figure out the measurement of the third side! We can do this by using the Pythagorean Theorem. The Pythagorean Theorem states: a˛ + b˛ = c˛. In this formula, a and b are the legs of the triangle and c is the hypotenuse. We simply substitute the measurements of the triangle with the letters in the formula to get the answer.
Triangles can also be labelled as congruent and similar. Congruent triangles are triangles that have equal sides and equal angles. Similar triangles have equal angles but their sides are not equal, they are just the same ratio. It is important to know that if two triangles are congruent, then they are also similar. But if they are similar, it doesn't necessarily mean that they are congruent unless the ratio of all sides are 1:1.
The formula for finding the area of a triangle is ˝ of the base times the height. Therefore, we must know the base and height in order to calculate the area which is always expressed in square units (e.g. square inches, square meters/metres...). The height of a triangle is the distance from its highest point to its base measured by a perpendicular line. The base is the side of the triangle that the height is perpendicular to.
By understanding the basic concepts of triangles, students will have a better understanding of geometric principles.
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Tutorgiant.com provides Triangle lessons with worksheets.
See some of the lessons in our video library.
ANGLES - Lesson (B) Angles in a Triangle (Grade 7)
TRIANGLES - Lesson (A) Angles and Triangles (Grades 4-5)
TRIANGLES - Lesson (B) Triangles and Side Lengths (Grades 4-5)
TRIANGLES - Lesson (C) Pythagorean Theorem (Grades 7-8)
TRIANGLES - Lesson (D) Triangle Inequalities (Grades 7-8)
TRIANGLES - Lesson (E) Special Segments in Triangles (Grade 9)
TRIANGLES - Lesson (F) The Converse of the Pythagorean Theorem (Grades 7-8)
TRIANGLES - Lesson (G) Congruent Triangles - AAS, HL (Grade 9)
TRIANGLES - Lesson (G) Congruent Triangles - SSS, ASA, SAS (Grade 9)
AREA - Lesson (E) Area of a Triangle (Grades 7-8)
NETS - Lesson (A) Nets of Pyramids and Prisms (Grades 4-6)
VOLUME - Lesson (C) Volume of Rectangular and Triangular Prisms (Grade 6)
Learn'Em Good
Math
by Stuart Ackerman
MSc.Ed.,B.A.
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