Answer:
Exterior Angle Inequality Theorem
An exterior angle of a triangle is the angle formed between any side of the triangle and an external extension of the adjacent side. There are six external angles formed in a triangle, two at each of the vertexes.
Exterior Angle
The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than both of the non-adjacent interior angles. This rule is satisfied by all the six external angles of a triangle.
Exterior Angle Inequality theorem
In the image above, we can see that angle ACD is an external angle. So,
Exterior Angle Inequality
and
Exterior Angle Inequality
Triangle Inequality Theorem
A triangle cannot be formed by just any set of three random lines. All triangles must observe the triangle inequality theorem. It states that the sum of lengths two sides of the triangle will always be greater than the length of the third side. This rule is satisfied by all the three sides of a triangle. It means if we have the lengths of two sides, we can safely bet that the length of the third side will be smaller than the sum of the two sides.
triangle inequality theorem
In the image, there are three inequalities,
triangle inequality theorem
triangle inequality theorem
triangle inequality theorem
Let's try to draw an imaginary triangle with sides 3cm, 4cm, and 10cm. We can see that 4 + 10 > 3, 3 + 10 > 4, but 4 + 3 < 10. Therefore, the sides with these dimensions do not follow the triangle inequality theorem. Hence, a triangle like this cannot exist.
Angle-Side Relationship
In a triangle, the angle opposite a longer side will be greater than the angle opposite a shorter side. Let's look at the angle-side relationship in a triangle that has three unequal sides, with AC being the smallest and BC being the longest.
angle side relationship
In this image, there are three inequalities that exist-
angle-side relationship
angle-side relationship
Step-by-step explanation:
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