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Helvetica is the font used in the Subways and in gap adds. You can tell it is Helvetica because the “a” looks like a drop. Geometry Journal 3 Helvetica was founded in Switzerland, there is a move about it on Netflix, you should watch it, its called “Helvetica”. It is a really good film. This font is Helvetica, the most used font in the world at this time. Maria Maldonado Hempstead 9-4 Parallel Lines, Parallel Planes, and Skew Lines What are Parallel Lines? Parallel lines are two lines on the same plane that never intersect. What are Parallel planes? Parallel Planes are planes that Never Intersect. What are Skew Lines? Slew Lines are lines that are not coplanar and will never intersect. What is a Transversal? A Transversal is any line that intersects two other lines at any 2 points. Angles That Get Formed When You Have a Transversal Corresponding Angles: <1 and <5 1 Alternate Exterior Angles: <1 and <8 and <2 and <7 2 3 4 5 6 7 8 Alternate Interior Angles: <5 and <4 and <3 and <6 Consecutive Interior Angles: <3 and <5 and <4 and <6 Corresponding angle Postulate and Converse If two Parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Converse If corresponding angles are congruent, then two parallels were cut by a transversal. Angle one and 5 are corresponding, there fore Since angle one has a measure of 80 degrees, so does angle 5. 1 5 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Converse If two coplanar lines are cut by a transversal, so that a pair of alternate interior angles are congruent, then the two lines are parallel. Angle 3 and angle 6 are congruent, because they are alternate interior angles. Angle 4 and angle 5 are congruent, because they are alternate interior angles. 3 4 5 6 Same Side Interior Angles Theorem If Two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. If two coplanar lines are cut by a transversal so that a pair of same side interior angles are supplementary, then the two lines are parallel. Angle 3 and angle 5 are congruent Angle 4 and angle 6 are Congruent 3 4 5 6 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. Converse If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel. Angle 1 and angle 8 are Congruent Because they are alternate exterior. Angle 2 and angle 7 are congruent too, Because they are alternate exterior. 1 2 7 8 Perpendicular Transversal Theorems In a plane, if a transversal is congruent to one of two parallel lines, then it is perpendicular to the other line. Since Perpendicular lines create a 90 degree angle with the line they intersect, then the other lines will be have the same slope but it will be Opposite and reciprocal. Transitive Property Transitive property: a=b and b=c so a=c How does it apply to parallel lines? If one line is the same as the other, then it will be parallel. How does it apply to perpendicular lines? Perpendicular lines are the same line, but they are opposite reciprocals. Black and Yellow • How Transitive property relates to parallel lines: Since these two lines are equal. • How Transitive property relates to perpendicular lines: Since these are perpendicular, they have opposite, reciprocal slopes. How Do you Find Slope? Slope is the measure of the steepness of a line. Y1-Y2 X1-X2 This is the formula to find the slope of a line. Parallel Lines will always have the exact Same slope, and two lines that are perpendicular will have opposite, reciprocal slopes. 3 Examples of Slopes of Lines Coordinates: (7, 9) (5, 3) m= 9-5 7-3 m= 4/4, or 1 Coordinates: (4, -2) (-6, -3) m= -2-3 4-6 m= 5/2 Coordinates: (8, 4) (6, 2) m=4-2 8-6 m= 2 Slope Intercept Form Slope Intercept form of a line is Y=mx+b. m= slope b= y intercept Ex. Y=4/3x+7 Ex. Y=7x+5 Ex. Y=56x-3 Point Slope Form Y-Y1=m(X-X1) How do you graph that????!!! M= slope Y1= your Y1 coordinate, X1= your X1 coordinate. So, put your first point at your X1, Y1 point and then graph the slope (m). Ex. Ex. Ex. Y-2=-3/5(x+3) Y-5=9/1(x+4) Y+4=7/8(x-3) Point: (-3, 2) Point: (-4, 5) Point: (3, -4) Slope:-3/5 Slope: 9/1 Slope:7/8 Note: To graph they x and y values in the equation, you must reciprocalize them.