The Magical Triangle Theorems And Congruence

In this triangle, the arrow shows that the largest side length is across from the largest angle.

These triangles are also congruent because they are also exactly the same. They have the same angles, side lengths, and are the same shape.

The Triangle Inequality Theorem states that both the smaller sides of a triangle have to add up to equal or be greater than the largest side

In these examples, the side lengths are: 5, 5, 7 and 4, 7, 8 with 7 being the longest in example 1 and 8 being the longest in example 2. The 2 smaller sides (5 and 5 / 4 and 7) both add up to 10 (example 1) and 11 (example 2), which, is greater than the longest sides in each of these triangles.

This theorem states that the, for example, smallest side of a triangle is across from the smallest angle.

The Triangle Sum Theorem states that the sum of all the angles in a triangle have to add up to 180°

Being congruent means that 2 objects MUST be exactly the same

When each angle is added, they equal 180°&nbsp;

-Equilateral Acute -Isosceles Right -Scalene Obtuse -Isosceles Acute -Scalene Acute -Isosceles Obtuse -Scalene Right

These 2 triangles are congruent because they're both exactly the same. Their angles, side lengths, and shape are all the same.

The Magical Triangle Theorems And Congruence

This arrow shows that the smallest side length is across from the smallest angle.

This arrow shows that the middle sized side length is across from the middle sized angle.

Examples Of All Triangles

Key (O) = Obtuse (A) = Acute (R) = Right

The reason this is an example (previous page), is because this triangle's angles add up to 180°, like the theorem states.

This is a book about the maths, yes maths, of geometry theorems for triangles

In this non-example, the side lengths are: 5, 5, 13, with 13 being the longest. The reason this is not a triangle is because the 2 smaller side lengths (5 and 5) do NOT equal 13, the longest side length

These triangles are not congruent because they are not the same. They don't have the same angles, side lengths, or shape.

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