Congruent Triangles
Topics
Introduction to :
"What's in a triangle? That which we call a threesided polygon
By any other name would look as such."
–Euclid, GeometRomeo and JuliOmetry
In this particular quote, Euclid (who wrote plays about shapes in Elizabethan English when he wasn't studying geometry) asks what makes the name "triangle" so special. After all, we can call a triangle anything we want and it would still be the same shape, right?
While that's true, these particular polygons are called triangles for very good reasons. If we split up the name into "tri" and "angle," the meaning of the word becomes very clear. The "tri" is for three (like tripod or tricycle) and "angle" is for, well, angle.
Example 1
What is the measure of ∠DFE? What sort of triangle is ∆DEF?

Example 2
What is the measure of ∠BCD? What kind of triangle is ∆BCD? 
Example 3
Find the measure of ∠CHG. What kind of triangle is ∆CHG?

Exercise 1
Why can an obtuse triangle have only one obtuse angle?
Exercise 2
Why can a right triangle have only one right angle?
Exercise 3
Are all equilateral triangles isosceles?
Exercise 4
Are all isosceles triangles equilateral?
Exercise 5
A triangle with differing side lengths and angles of 82°, 92° and 6° is what kind of triangle?
Exercise 6
A triangle has at least two side lengths that are equal to each other and all three angles equaling 60°. What kind of triangle is it?