GEOMETRY FUNDAMENTALS - UNIT 11 Essays (556 words) - Geometry

GEOMETRY FUNDAMENTALS - UNIT 11 REVIEW SIMILAR POLYGONS Cosine ratioIn a right triangle, the side adjacent to an acute angle over the hypotenuse.Geometric meanFor any positive real numbers a, b, and x if then x is called the geometric mean between a and b.Projection of a point on a lineThe point where a perpendicular through the point to the line intersects the line.Projection of a segment on a lineThe portion of a line with endpoints that are the projections of the endpoints of the segment.ProportionAn equation that states that two ratios are equal.RatioThe comparison of two numbers by division. The quotient is the ratio of the two numbers.Similar polygonsPolygons whose vertices can be matched in a one-to-one correspondence so that corresponding angles are equal and corresponding sides are in proportion.Sine ratioIn a right triangle, the side opposite an acute angle over the hypotenuse.Tangent ratioIn a right triangle, the side opposite an acute angle over the side adjacent to the acute angle. P-15:If the three angles of one triangle are equal to the three angles of another triangle, then the triangles are similar. (AAA) Cross Product property If , then ad = bc . Equivalent Forms property . The cross product of each proportion gives the same equation, ad = bc . Denominator Sum property Denominator Difference property Numerator-Denominator Sum property 5-1:If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.5-2:If two sides of one triangle are proportional to two sides of another and the included angles are equal, then the triangles are similar.5-3:If three sides of one triangle are proportional to three sides of another, then the triangles are similar.5-4:Similarity of polygons is reflexive, symmetric, and transitive.5-5:If two polygons are similar, then the ratio of their perimeters is the same as the ratio of any pair of corresponding sides.5-6:If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the two sides proportionally.5-7:If a ray bisects an angle of a triangle, then it divides the opposite side into segments with lengths proportional to the lengths of the other two sides of the triangle.5-8:If two triangles are similar, then the lengths of corresponding altitudes have the same ratio as the lengths of any pair of correspon ding sides.5-9:If the altitude to the hypotenuse of a right triangle is drawn, then the two triangles formed are similar to each other and similar to the given triangle.5-10:In a right triangle the sum of the squares of the length of the legs is equal to the square of the length of the hypotenuse. (Pythagorean Theorem)5-11:If the sum of the squares of two sides of a triangle equals the square of the third side, then the triangle is a right triangle.5-12:In a 30-60-90 triangle, the hypotenuse is twice the short leg, and the longer leg is times the short leg5-13:If each acute angle of a triangle is 45, then the measure of the hypotenuse is times the leg.