Postulates&Theorems Unit 4
Lesson 1
Hinge Theorem~ If two corresponding legs of one triangle are equal to two corresponding legs of another triangle and the angles included in the triangle are not equal, then the third side across from the greater included angle will be greater.
I chose the Hinge Theorem because it is quite important in terms of comparing triangles together and to make sure that you are not misconstrued when you find two congruent legs on a triangle.
I chose the Hinge Theorem because it is quite important in terms of comparing triangles together and to make sure that you are not misconstrued when you find two congruent legs on a triangle.
Lesson 2
Product Property of Square Roots~ If given nonnegative numbers a and b, the square root of the product of a and b- ab is equal to the square root of a times the square root of b, eventually giving an equality property use.
I chose the Product Property of Square Roots because it is significant to avoid computation errors when using radicals to solve problems concerning Pythagorean Theorem, special triangle properties, etc. It also helps make dividing and multiplying by radicals much easier.
In the diagram, the side across from the 60 degrees is sqrt{3} times the other leg. Therefore, you must do 5sqrt{2} x sqrt{3}. This will therefore equal 5srqt{6} because of the Product Property of Square Roots.
I chose the Product Property of Square Roots because it is significant to avoid computation errors when using radicals to solve problems concerning Pythagorean Theorem, special triangle properties, etc. It also helps make dividing and multiplying by radicals much easier.
In the diagram, the side across from the 60 degrees is sqrt{3} times the other leg. Therefore, you must do 5sqrt{2} x sqrt{3}. This will therefore equal 5srqt{6} because of the Product Property of Square Roots.
Lesson 3
Pythagorean Theorem~ In a right triangle, the sum of the legs squared is equal to the square of the hypotenuse. This results in a equation - a^2+b^2=c^2. a and b are both the legs while the c is a hypotenuse.
I chose the pythagorean theorem as it is one of the focal stepping stones of triangles and geometry. This theorem helps us understand right triangles and how the angles and sides work together to prove statements.
I chose the pythagorean theorem as it is one of the focal stepping stones of triangles and geometry. This theorem helps us understand right triangles and how the angles and sides work together to prove statements.
Pythagorean Inequalities Theorem~ In △ABC, c is the length of the longest side/hypotenuse. If c^2 is greater than a^2+ b^2, then △ABC is an obtuse triangle. If c^2<a^2+b^2, then △ABC is an acute triangle.
I chose this because this theorem helps find what type of triangle 3 sides can create just by being given the lengths. It is very helpful in geometry and in real world application.
I chose this because this theorem helps find what type of triangle 3 sides can create just by being given the lengths. It is very helpful in geometry and in real world application.
Lesson 4
30°-60°-90° Triangle Theorem~ In a 30°-60°-90° triangle, the length of the longest side/hypotenuse is twice the length of the shortest leg(across from the 30°), and the length of the longer leg(across from the 60°) is the length of the shorter leg times \sqrt{3}.
I chose this because it is one of the essential special triangle types. This type of triangle will come up a lot in geometry, and it is important to know the rules of the triangle. It can also be used in real world applications with constructions and architecture.
I chose this because it is one of the essential special triangle types. This type of triangle will come up a lot in geometry, and it is important to know the rules of the triangle. It can also be used in real world applications with constructions and architecture.
Lesson 5
Converse of the Pythagorean Theorem~ If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side(a^2+b^2=c^2), then the triangle is a right triangle. Basically proves opposite statement of the pythagorean theorem.
I chose this because this theorem is very important in determining types of triangles. If there are diagrams not drawn to scale you can differentiate if its a right triangle or not by using this theorem. It goes hand in hand with the pythagorean theorem which makes this theorem essential to understand all the aspects of the pythagorean theorem.
I chose this because this theorem is very important in determining types of triangles. If there are diagrams not drawn to scale you can differentiate if its a right triangle or not by using this theorem. It goes hand in hand with the pythagorean theorem which makes this theorem essential to understand all the aspects of the pythagorean theorem.