Download U2D3-Classifying Triangles

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Classifying Triangles
Triangles can be classified by the lengths of their sides, or by their angles. For the
purpose of this lesson, we will mainly focus on the side-length classifications:
Scalene –
Isosceles –
All sides are different lengths (all angles are different).
The triangle has two identical side lengths (angles at the base of those
sides are identical)
Equilateral – The triangle has three identical side lengths (all three angles are the same)
If you are given the three vertices of a triangle, you can find the lengths of the sides by
using the length of a line segment formula. l 
x2  x1 2   y2  y1 2
Ex.1. ∆DEF has vertices D(1, 7), E(3, 4) and F(6, 6).
a.
Classify the triangle by side length
b.
Determine the perimeter of the triangle, to the nearest tenth of a unit.
Triangles can also be classified by angles
Acute Triangle – Three angles less than 90 degrees.
Obtuse Triangle – One angle greater than 90 degrees.
Right Triangle – One angle equal to 90 degrees.
For now, we won’t worry about acute or obtuse triangles. However, we can tell if a
triangle is a right triangle based on the slopes of the line segments that make up the
triangle.
If two of the line segments are perpendicular (slopes are negative reciprocals), then it is a
right triangle.
Ex.2. ∆ABC has vertices A(1, 7), B(3, 4) and C(6, 6).
a)
Show whether or not it is a right-angled triangle by using the slopes of the
line segments.
b)
Calculate the side lengths. Do they fulfil the Pythagorean relation?
c)
Find the area of the triangle
Homework – Pg. 72. Q. 5,7,8,9,10