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Transcript of Geometry
and functions... For every Y value, there is a unique X value in order to be a function! There are also four congruence postulates used to prove congruence within triangles... SIDE-SIDE-SIDE (SSS) CONGRUENCE: triangles are congruent if all 3 corresponding sides of two triangles are equal in length SIDE-ANGLE-SIDE (SAS) CONGRUENCE: triangles are considered congruent if any pair of corresponding sides and the included angles are congruent ANGLE-SIDE-ANGLE (ASA) CONGRUENCE: triangles are considered congruent if any pair of corresponding angles and their included sides are congruent ANGLE-ANGLE-SIDE (AAS) CONGRUENCY:triangles are considered congruent if two pairs of corresponding angles and a pair of opposite sides are congruent And in case you were wondering... ...NO... ...there is no ASS postulate!!! PERPENDICULAR LINES: two lines that intersect at 90 degree angles CONSTRUCTION: the creating of angles, lengths, and other geometric figures using a straight edge and a compass DILATION: a similarity transformation in which the figure is reduced or enlarged without changing the center and using a scale factor other than zero DILATION NOTATION: a formula used to show the scale factor and the point of origin of a dilation Dk (x, y) = (kx, ky) SCALE FACTOR: a number used as a factor to determine the scale to which a figure is dilated or enlarged SIMILARITY: two objects that are the same shape ANGLE-ANGLE (AA) SIMILARITY: all corresponding angles are equal TRANSFORMATION: changes the position of a shape on a coordinate plane There are three types of rigid (non-dilated) transformations... REFLECTION (FLIP): the figure is reflected over a sustained line of reflection TRANSLATION (SLIDE): every point in the pre-image is moved the same distance and same way to create a new image without changing the original image ROTATION: a transformation that turns a figure around a fixed point CIRCLE CIRCUMFERENCE:the boundary line of a circle, found by using pi AREA OF A CIRCLE: the area enclosed by a circle CENTRAL ANGLE: an angle whose vertex is at the center of a circle INSCRIBED ANGLE: formed by two chords in a circle which have a common endpoint QUADRILATERAL: a polygon with four sides whose sum of interior angles equals 360 degrees KITE: a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other TRAPEZOID: a convex quadrilateral with at least one pair of parallel sides RHOMBUS: an oblique-angled equilateral parallelogram ; any equilateral parallelogram except a square PARALLELOGRAM: a quadrilateral with two pairs of parallel sides RECTANGLE: a parallelogram all of whose angles are right angles; especially: one with adjacent sides of unequal length SQUARE: has four equal sides and four equal angles TRIANGLES PYTHAGOREAN THEOREM: The theorem that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse THERE ARE TWO TYPES OF SPECIAL RIGHT TRIANGLES... 30-60-90 TRIANGLE And the 45-45-90 TRIANGLE Haha... not really... TRIGONOMETRY: The branch of mathematics that deals with the relationships between the sides and the angles of triangles and the calculations based on them, calculated with sine, cosine, and tangent TANGENT: the tangent of a triangle is found by dividing the opposite side of the triangle by the adjacent side of the triangle SINE: the sine of a triangle is found by dividing the opposite side by the hypotenuse LAW OF SINES: law stating that the ratio of a side of a plane triangle to the sine of the opposite angle is the same for all three sides COSINE: the cosine of a triangle is found by dividing the adjacent side of a triangle by the hypotenuse Math is used every day in the real world in order to help our imperfect society appear to work as a well-oiled machine.
Angles are used for architecture and for playing pool. Finding bisectors and midpoints are also used in architecture as well as cutting a cake into equal pieces. Congruence is used every day to compare sizes of clothes between girlfriends and also in shoes. Constructions are used in order to recreate images and to let people feel smart using a compass. Transformations, dilations, and vectors, are used in order to help understand where to move things and how to move them. Circles are used in order to measure the distance around planets and other unnaturally shaped, circular objects in nature. Trigonometry is used in order to help solve missing triangle sides and angles. Quadrilaterals are used all the time because they are more pleasing to the eye and they are one of the simplist shapes to draw. And because they are so simple, we need to learn all of the long and complicated properties in order to help us feel and look smarter. Triangles are used in life because what better way to learn about the dimensions of a star fish? Or a pizza slice? Lines are used in order to help outline things and to make roads straighter and safer for the community, therefore causing less road-related accidents and fatalities.