Unit 4 -Meredith Derucki
Unit 4 is about triangles. How to find the hypotenuse of triangles, how to classify triangles by angles and sides, how to find which angles in a triangle are bigger based on side and the opposite, and so many more things on how to apply all our knowledge. All of the postulates and theorems we have learned this unit helped us gather what we need to further apply certain aspects of triangles.
Hinge Theorem:
If two sides of a triangle are congruent to two sides of another triangle, but the included angles of those sides are not congruent, then the side opposite the larger angle will be longer than the other third side of the triangle. The converse of this theorem is if you have two sides congruent to two sides of another triangle and the third side of one triangle is longer than the other, the opposite angle of the longer side will be larger than the matching one in the other triangle. |
Pythagorean Theorem:
With a right triangle, the sum of the squares of the lengths of the legs of the triangle is equal to the square of the length of the hypotenuse. Equation: a^2 + b^2 = c^2 Converse Pythagorean Theorem: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the lengths of the third triangle then the triangle is proven to be a right triangle. |
All of the postulates chosen were important in their own way. What they all have in common is that they are the base of adding more and more into your learning. The base of the Pythagorean Theorem branches off to for the Converse of Pythagorean Theorem and the Pythagorean Inequalities Theorem. The 45-45-90 and 30-60-90 Triangle Theorems are helpful when trying to find lengths of the sides and also help your skill of determining which sides are longer than which sides. Hinge Theorem helps you understand side lengths and how triangles will be shaped. The Triangle Inequality Theorem helps you know what a triangle can and cannot be. Overall, these postulates and theorems help us in ways that will help us better understand Geometry and our learning later to come in math.