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Geometry—Segment 2 Reference Sheet Module 6 Use distance formula and slope formula to classify triangles: ° Classifying by angles: acute, right, obtuse ° Classifying by sides: equilateral, isosceles, scalene ° Slope-intercept form: y=mx+b, where b is the y-intercept and m is the slope. ° Point-slope form: y – y1 = m(x – x1) where (x1,y1) is a given point on the line and m is the slope ° Parallel lines are two lines that lie within the same plane and never intersect. Parallel lines have slopes that are equal. ° Perpendicular lines are two lines that intersect at 90-degree angles. Perpendicular lines have slopes that are opposites and reciprocals and the product of the slopes is always –1. (also, undefined and zero slope lines) Properties of Parallelograms - Both pairs of opposite sides are congruent and parallel - The diagonals bisect each other - Both pairs of opposite angles are congruent - Consecutive angles are supplementary Properties of Rectangles - ALL PROPERTIES OF A PARALLELOGRAM PLUS… - Contains four right angles - The diagonals are congruent Properties of Squares - ALL PROPERTIES OF A RECTANGLE PLUS… - All four sides are congruent - The diagonals are perpendicular - The diagonals bisect the angles - Example of parallel lines: y= 2/3x + 2 and y= 2/3x –4. - Example of perpendicular lines: y= 2/3x – 1 and y= -3/2x -3. ° Dividing segments into given ratio: The ratio 1:4 is read “one to four.” If you were asked to find the distance that is at a ratio of 1:4 between two points, this would mean the same as splitting the distance into 1 + 4 or 5 equal pieces and then finding 1 of those pieces. ° Perimeter: the distance around the figure. ° Area of a polygon: the space inside the boundary of a 2-dimensional object Properties of Rhombi - ALL PROPERTIES OF A SQUARE EXCEPT... - Does NOT have four right angles - Does NOT have congruent diagonals Properties of Trapezoids - Exactly one pair of parallel sides - Consecutive angles between the bases are supplementary - Two special types: right and isosceles Properties of Kites - Two pairs of adjacent, congruent sides - Non-vertex angles are congruent - Diagonals are perpendicular - Non-vertex diagonal is bisected Module 7 SOH—CAH—TOA Pythagorean Theorem CHO—SHA—CAO Angle of Elevation: an angle at which an observer must direct his or her line of sight in an upward motion to view an object. Angle of Depression: an angle at which an observer must direct his or her line of sight in a downward motion to view an object. Geometry—Segment 2 Reference Sheet Module 8 ° Volume: The ratio between the corresponding sides of two similar solids can be represented in general terms by a:b (read "a to b") or a/b. The ratio of the volumes of similar solids can be represented by the ratio a 3:b3 or a3/b3 . Circles ° Calculate circumference using: C = ∏d or C = 2∏r ° Calculate area using: A = ∏r2 ° Percent of Change: change in dimensions can be represented by a scale factor, a proportion, a ratio, or by a percent of change. ° Density: a ratio of mass to area or volume. ° Cavalieri’s Principle: if the area of the cross sections of two 3-D figures are congruent and the height of the figures is also congruent, then it can be concluded that the volumes of the two figures are congruent. Cone ° Volumecone = ⅓∏r2h ° Mass: how much matter is in an object Cylinder ° Volumecylinder = ∏r2h Sphere ° Volumesphere = 4/3∏r3 Module 9 ° circle - the set of all points that are the same distance away from a fixed point ° radius - the distance between the center of a circle and any point on the circle ° chord - a segment on the interior of a circle whose endpoints are on the circle Pyramid ° Volumepyramid = ⅓(B)(h) ° (B) Base = L x W All circles have an equation. From its equation, we can determine the center and the radius of the circle in order to graph it. Equation of a Circle: (x–h)2 + (y–k)2 = r2 where (h, k) is the center and r is the radius. ° diameter - a chord that passes through the center of the circle ° circumference - the distance around the circle ° secant - a line that intersects a circle in two places ° arc - one section of the circumference of a circle ° arc length - the distance between two points on a circle ° minor arc - an arc measuring less than 180° A circumscribed circle is a circle that surrounds a polygon and intersects each one of its vertices. Construct Perpendicular Bisectors An inscribed circle is a circle that is contained within the interior of a polygon and intersects each side of a polygon exactly one time at a 90° angle. Construct Angle Bisectors Concentric Circles— Circles that share a common center. Arc Length = derived from the formula for the circumference of a circle. Arc length = where x is the measure of the central angle. Area of Sector = derived from the formula for the area of a circle. Area of a sector = where x is the measure of the central angle. Radians = Another unit of measure (other than degrees) to Inscribed Quadrilateral Theorem = The opposite angles of an inscribed quadrilateral to a circle are supplementary.