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This document discusses four ways to prove that two lines are parallel using a transversal that intersects the lines. Specifically, it states that if corresponding angles, alternate interior angles, consecutive interior angles, or alternate exterior angles are congruent when two lines are cut by a transversal, then the two lines must be parallel.
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This document discusses properties of parallel lines cut by a transversal. It introduces two postulates about corresponding angles being congruent if lines are parallel, and lines being parallel if corresponding angles are congruent. It then presents four theorems: if alternate interior angles or same-side interior angles of two lines cut by a transversal are congruent/supplementary, the lines are parallel; and if two lines are perpendicular to the same line, they are parallel. Finally, it lists five ways to prove two lines are parallel using the previous postulates and theorems.
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This document outlines five theorems related to parallel lines cut by a transversal: 1) the corresponding angles postulate states corresponding angles are congruent, 2) the alternate interior angles theorem states alternate interior angles are congruent, 3) the consecutive interior angles theorem states consecutive interior angles are supplementary, 4) the alternate exterior angles theorem states alternate exterior angles are congruent, and 5) the perpendicular transversal theorem states if a transversal is perpendicular to one parallel line, it is perpendicular to the other.
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This document provides instructions for solving right triangles using trigonometric functions. It explains that solving a right triangle involves finding the measures of the three angles and lengths of the three sides. It notes that a calculator's inverse trigonometric functions allow working backwards from a trig ratio to the corresponding angle measure. Finally, it offers guidance for determining which inverse function to use based on the given information, such as using tangent when the hypotenuse is unknown or cosine when the opposite side is missing.
6.5 terms
This document defines and provides key details about trapezoids, isosceles trapezoids, the midsegment of a trapezoid, and kites. It states that a trapezoid has one pair of parallel sides called bases, and the other sides are called legs. An isosceles trapezoid has congruent legs and congruent base angles. The midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. A kite has two pairs of consecutive congruent sides but opposite sides are not congruent, and its diagonals are perpendicular with one pair of opposite angles being congruent.
11.5 terms
The document discusses calculating the areas of circles and sectors. It states that the area of a circle is calculated as A = πr2, and the area of a sector is calculated as (Arc Measure/360)(area of the full circle), which finds the percentage of the total circular area that the sector represents by dividing the arc measure in degrees by 360.
11.1 terms
The document discusses angle measures in polygons. It states that the sum of interior angles in any polygon is (n-2)180, where n is the number of sides. It also explains that the sum of exterior angles is always 360, and each exterior angle is calculated as 360/n, where n is again the number of sides.
11.4 terms
This document discusses formulas for circumference and arc length. It states that circumference C equals 2πr or πd, where r is the radius and d is the diameter. It also explains that arc length is calculated as a percentage of the circumference by taking the arc measure in degrees and dividing by 360, then multiplying that fraction by the circumference.
9.5 terms
This document provides information about trigonometric ratios and using a calculator to evaluate trigonometric functions. It defines the sine, cosine, and tangent ratios using the SOHCAHTOA mnemonic. It also explains that calculators may require typing the trig function before or after the number, and some may not require hitting the equals sign, so it is important to know how to use the specific calculator.
10.6 terms
The standard equation for a circle is (x-h)2 + (y-k)2 = r2, where (h,k) represents the center of the circle and r represents the radius. When solving for the center or radius, the terms in the parentheses change signs - the x and y terms change to the opposite of the center coordinates h and k, and the radius r is the square root of the number after the equals sign.
8.1 terms
A ratio is a fraction that compares two quantities, such as the ratio of a to b written as a/b. A proportion is when two ratios are equal to each other, allowing the fractions to be cross-multiplied and canceled out. Ratios and proportions use fractions to compare relationships between quantities.
6.6 terms
This document presents a hierarchy of quadrilaterals in a grid structure, with each shape below sometimes being a type of the shape above it, and each shape above always being a type of the shapes below it since they share characteristics. Kite is at the top and is sometimes a parallelogram, rectangle, square, rhombus or trapezoid. Parallelogram is sometimes a rectangle, square or rhombus. Trapezoid is sometimes an isosceles trapezoid.
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- 1. Terms of Endearment Proving Lines are Parallel: 3.4