SAMPLE College Math

‭Based‬ ‭on‬ ‭these‬ ‭properties‬ ‭of‬ ‭angles,‬ ‭triangles‬ ‭are‬ ‭also‬ ‭classified‬ ‭as‬ ‭acute‬ ‭triangle‬ ‭(wherein‬ ‭all‬ ‭three‬ ‭angles‬ ‭of‬ ‭the‬ ‭triangle‬ ‭are‬ ‭acute),‬ ‭right‬ ‭triangle‬ ‭(one‬ ‭angle‬ ‭of‬ ‭the‬ ‭triangle‬ ‭is‬ ‭a‬‭right‬‭angle),‬‭and‬‭obtuse‬ ‭triangle‬ ‭(one‬ ‭angle‬ ‭of‬ ‭the‬‭triangle‬‭is‬‭an‬‭obtuse‬‭angle).‬‭It‬‭should‬‭also‬‭be‬‭noted‬‭that‬‭the‬‭sum‬‭total‬‭of‬‭all‬ ‭three‬‭angle‬‭of‬‭the‬‭triangles‬‭should‬‭always‬‭be‬‭equal‬‭to‬‭180‬ ‭0‬ ‭.‬‭The‬‭different‬‭types‬‭of‬‭triangles‬‭categorized‬ ‭on angles are given as follows:‬

‭Triangles‬ ‭can‬ ‭also‬ ‭be‬ ‭categorized‬ ‭on‬ ‭the‬ ‭basis‬ ‭of‬ ‭their‬ ‭sides,‬ ‭and‬ ‭are‬ ‭termed‬‭as‬‭scalene‬‭(none‬‭of‬‭the‬ ‭sides‬ ‭of‬ ‭the‬ ‭triangle‬ ‭are‬ ‭congruent‬ ‭or‬ ‭same),‬ ‭isosceles‬ ‭(two‬ ‭sides‬ ‭of‬ ‭the‬ ‭triangle‬ ‭are‬ ‭congruent),‬‭and‬ ‭equilateral‬ ‭(when‬ ‭all‬‭three‬‭sides‬‭of‬‭the‬‭triangle‬‭are‬‭congruent).‬‭The‬‭classification‬‭of‬‭triangles‬‭based‬‭on‬ ‭sides is shown here:‬

‭Triangle‬‭inequality‬‭theorem‬ ‭states‬‭that‬‭the‬‭sum‬‭of‬‭two‬‭sides‬‭of‬‭any‬‭triangle‬‭will‬‭always‬‭be‬‭greater‬‭than‬ ‭the‬ ‭third‬ ‭side.‬ ‭For‬ ‭instance,‬ ‭a‬ ‭triangle‬ ‭cannot‬ ‭be‬ ‭formed‬ ‭if‬ ‭its‬ ‭sides‬ ‭are‬ ‭measured‬ ‭as‬ ‭5cm,‬ ‭7cm‬ ‭and‬ ‭13cm, since adding two sides: 5+7 is not greater than the third side, that is, 13cm.‬ ‭Area of a triangle:‬ ‭The area of the triangle can be‬‭found by using the following formula:‬ ‭ ‬‭‬‭ ‬‭‬‭ ‬ = ‭1 ‭2 ‬ ‬ * ‭ ‬ * ‭ℎ ℎ ‬= ‭ ‭2 ℎ ‬ ‬ ‭The‬ ‭perimeter‬‭of‬‭the‬‭triangle‬ ‭can‬‭be‬‭found‬‭by‬‭adding‬‭the‬‭measure‬‭of‬‭all‬‭three‬‭sides‬‭of‬‭a‬‭triangle,‬‭that‬‭is‬ ‭P = a + b + c‬ ‭Pythagorean‬ ‭Theorem:‬ ‭This‬‭theorem‬‭is‬‭applicable‬‭only‬‭to‬‭right‬‭angle‬‭triangle.‬‭As‬‭per‬‭the‬‭Pythagorean‬ ‭Theorem,‬‭the‬‭square‬‭of‬‭the‬‭hypotenuse‬‭of‬‭the‬‭triangle‬‭is‬‭equal‬‭to‬‭the‬‭square‬‭of‬‭the‬‭other‬‭two‬‭sides‬‭of‬‭the‬ ‭triangle.‬ ‭The‬ ‭side‬‭opposite‬‭to‬‭the‬‭right‬‭angle‬‭of‬‭the‬‭right‬‭angle‬‭triangle‬‭is‬‭known‬‭as‬‭the‬‭hypotenuse.‬‭In‬ ‭the given triangle,‬

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