Angle realationships:

some angle relationships that i have encountered are corresponding angles, alternate interior angles, same side interior angles, alternate exterior angles, same side exterior angles, and vertical angles.

coresponding angles are when angles are on the exterior and interior on the same side.

Alternate interior angles are when two angles are on the interior and on different sides of the transversal.

Same side interior angles are when two angles are in the interior on the same side.

alternate exterior angles are when two angles are on different sides of the transversal on the exterior.

same side exterior angles are when the two angles are on the same side of the transversal on the exterior.

vertical angles are on the exterior and interior and are vertical from each other.

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Angles in a triangle:

Angles in a triangle all ways equal 180 degrees when you add all three of the up. For example if there is a triangle with one angle of 80 and another one is 50 degrees the missing angle would be 50 degrees because 50+50+80=180 . As you can see finding the missing angles of a triangle is fairly easy because it will all ways equal 180 degrees when you add them.

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triangle inequality:

based on the type of triangle the three side lenthgs are different. Also the two small sides areas added together make the area of the biggest side or the hypotenuse in any triangle. For example if one side was 10 squared and one side was 15 squared the the hypotenuse would be 18 squared because it would be equal to the sum of the areas of the two legs. If the three sides made a triangle then then the two areas of the legs added together would equal the are of the hypotenuse however if the three sides did not make a triangle then that means the two areas of the legs did not equal the area of the hypotenuse when added together. Three sides would not make a triangle if the areas of the two legs did not equal the are of the hypotenuse when added together. Three sides will make a triangle if the areas of the two legs equal the area of the hypotenuse.

triangle side length patterns:

some patterns i see of the acute triangles is if the sum of the small and medium areas added together is bigger than the laege area it is an acute triangle. I also see that if the two legs areas are added together and the sum is smaller than the area of the largest side then it is an obtuse angle. In order to form a right triangle the areas of the two smaller sides added together needs to be equal to thenarea of the largest side.

If 3 squares have sides that make an acute triangle, the sum of the areas of the 2 small squares must be bigger than the area of the large side.

If 3 squares have sides that make an obtuse triangle, the sum of the areas of the 2 small squares must be smaller than the area of the biggest side

If 3 squares have sides that make a right triangle, the sum of the areas of the 2 small squares must be equal to the area of the biggest side.

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square roots:

a square root is the number you get when you multiply a number by itself. For example the square root of 4 is 2 because 2 times 2 is 4. To estimate a non-perfect square root to the nearest tenth you need to look at the number after the decimal and if it is 5 and above you go up one whole number but if it is 4 or lower you go one whole number down. Perfect squares are when the square of a number is a whole number and no decimals.

 

Pythagorean theorem:

The Pythagorean theorem Is how to find either the missing hypotenuse or leg of a right triangle. To find the missing hypotenuse first calculate the area of both legs then you square that answer then thats the missing length of the hypotenuse. Now to find the missing leg you must calculate the area of the hypotenuse then subtract the area of the one leg that is known from the area of the hypotenuse then you must square that number and thats your answer for the missing leg.

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