Blog 31: Angle Relationships

What angle relationships have I learned about? Some of the angle relationships I’ve learned was corresponding angles which are angles that are exterior and interior angles. Another one is vertical angles where they are diagonal from each other. Same side interior angles are the ones that have both interior which means inside the parallel lines and on the same transversal. Same side exterior angles are the ones that are on the outside of the parallel lines and on the same transversal. Alternate exterior angles are the ones that are both exterior but they are on different sides of the transversal. Last but not least, the alternate interior angles are the interior but on different sides of the transversal.

Blog 32: Angles in a Triangle

When finding a sum of a triangle you need to equal all of the sides to 180. For example, if you have 25 and 26 degrees but your missing one side you need to write it like this (x+25+26=180), but without the parenthesis. After you write it in that form you have to add 25+26 which is 51. Once you so that you have to subtract 51 from 180 so that way you leave x by itself and it is equaled to 129. So 129+25+26 equal 180 that is how you find the sum of x.

Blog 33: Triangle Inequality

What do I notice about how the three side lengths compare to each other? The small squares are way smaller than the larger square. An example is that if you use the numbers 4,8,12 that is an example. How are the lengths that did not form a triangle different from the ones that did? The lengths that made a triangle are similar than the lengths that don’t make triangles.

Blog 34: Triangle Side-Length Patterns

If three squares have sides that make an acute triangle, then the sum of the areas of the two small squares will be larger than the large squares. If three squares have sides that make and obtuse triangle, then the sum of the areas of the two small squares will be smaller than the large square. If three squares have sides that make a right triangle, then the sum of the areas of the two small squares will equal the larger square.

Blog 35: Square Roots

What is a square root? A square root is a number that produces a number when multiplied by itself. How can you estimate a square root? You can estimate it by looking at all the numbers that square itself and see what number is closer to the one being squared. After you do that you see which two numbers its between then it will have a decimal so it will be approximate. Some square roots will have a whole number because it can multiply by itself, while other numbers will have decimals because it can’t multiply the whole number by itself.

Blog 36: Pythagorean Theorem

You can use the pythagorean theorem when using right triangles that either are missing the leg or the hypotenuse. If you are missing the hypotenuse and you have both the legs then you have to find the area by squaring both the legs. After that, you have to add both the areas together and square root that answer. Once you get your answer then that is how you find the missing hypotenuse. If you are missing one of the legs then you square both the lengths and find the area. After you do that then you have to subtract them both and square root that answer to find the missing leg. The reason why you subtract it is because the hypotenuse is larger than the legs so you make the leg shorter by subtracting the two areas.