![]() ![]() ![]() Definition of Parallel Planes Planes that do not intersect. Definition of Parallel Lines Lines that lie on the same plane and do not intersect. Lines Perpendicular to a Transversal Theorem If two lines are perpendicular to the same line, then they are parallel to each other. Transitive Property of Parallel Lines If two lines are parallel to the same line, then they are parallel to each other. Perpendicular Postulate If there is a line and a point not on that line, then there is exactly one line that goes through the point perpendicular to the given line. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, consecutive interior angles are supplementary Corresponding Angles Converse If two lines are cut by a transversal and corresponding angles are congruent then the two lines are parallel Alternate Interior Angles Converse If two lines are cut by a transversal and Alternate Interior angles are congruent then the two lines are parallel Alternate Exterior Angles Converse If two lines are cut by a transversal and Alternate Exterior angles are congruent then the two lines are parallel Consecutive Interior Angles Converse If two lines are cut by a transversal and consecutive interior angles are supplementary then the two lines are parallel Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, alternate exterior angles are congruent. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, alternate interior angles are congruent. Linear Pair Perpendicular Theorem If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular Definition of Corresponding Angles Definition of Alternate Interior Angles Definition of Alternate Exterior angles Definition of Consecutive Interior Angles Corresponding Angles Postulate If two parallel lines are cut by a transversal, corresponding angles are congruent. I hope that this isn't too late and that my explanation has helped rather than made things more confusing.Vertical Angle Theorem Vertical angles are congruent Reflexive Property Symmetric Property Transitive Property Definition of Perpendicular Lines When two perpendicular lines intersect they create four right angles. ![]() You can then equate these ratios and solve for the unknown side, RT. If you want to know how this relates to the disjointed explanation above, 30/12 is like the ratio of the two known side lengths, and the other ratio would be RT/8. Now that we know the scale factor we can multiply 8 by it and get the length of RT: If you solve it algebraically (30/12) you get: I like to figure out the equation by saying it in my head then writing it out: In this case you have to find the scale factor from 12 to 30 (what you have to multiply 12 by to get to 30), so that you can multiply 8 by the same number to get to the length of RT. The first step is always to find the scale factor: the number you multiply the length of one side by to get the length of the corresponding side in the other triangle (assuming of course that the triangles are congruent). ![]()
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