Transcript Heidi
BY Leonard •I was unable to place the bar over the letters for a line segment. I hope you understand that where it is supposed to say segment AB, it just says AB. •Next to each key term, I placed a P, T, or Q to show what topic it is from. P stands for Parallelism, T stands for Triangles, and Q stands for Quadrilaterals • I had trouble picking what kind of background I would use for each slide, so I decided to make the background colorful and unique. Key Terms Skew lines: 2 lines that are in different planes and never intersect Parallel: when 2 lines are coplanar and never intersect Transversal: a line that intersects 2 parallel lines (T is the transversal in this diagram) Early Version of Exterior Angle Earl Warren Key Terms Continued Alternate interior angles: nonadjacent angles on the opposite sides of the transversal that are in the interior of the lines the transversal runs through Corresponding angles: angles on the same side of the transversal, but one angle is interior and the other is exterior. Del Mar’s Diagonal 15th Street More Key Terms a Quadrilateral: the union of 4 segments d b c Sides: segments of a shape (for example, AD & DC) Vertices: where the segments meet each other (a, b, c, d) Angles: the combination of two segments (such as ABC ) Convex: when a line is able to connect any 2 points in a plane or figure with out going out of the figure itself convex Encinitas Median Moonlight Beach Key terms continued Opposite (in terms of quadrilaterals): the description of sides that never intersect or angles that do not have a common side (such as AB &CD and AD & BC or A & C and B & D) Consecutive (in terms of quadrilaterals): the description of sides that have a common end point or angles that share a common side (E.g. AB &BC or D & C) Diagonal (in terms of quadrilaterals): segments joining 2 nonconsecutive vertices (AC & BD for example) Transversal Torrey Pines State Beach Parallelogram: quadrilateral with both pairs of opposites sides parallel Trapezoid: quadrilateral with one pair of parallel sides Bases (of a trapezoid): the parallel sides (AB & CD) Median (of a trapezoid): segment joining midpoints of nonparallel sides (the red line) Rhombus: a parallelogram with all sides congruent Rectangle: a parallelogram with all angles right angles Square: parallelogram with all congruent sides and all right angles Intercept: the term used to describe when points are on the transversal (Line A and B intercept segment CD on the transversal) Concurrent: when lines contain a single point which lies on all of them Point of Concurrency: the point which is contained by all of the lines PCA Corollary: states that corresponding angles created by 2 parallel lines cut by a transversal are congruent In other words: if L1 and L2 are parallel, then 3 and 4 are congruent This is possible because of the PAI Theorem and the Vertical Angle Theorem -ior In other words: Because AC and BD bisect each other, • A BCD is a parallelogram Theorem: If there is one right angle in a parallelogram, then it has 4 right angles, which means that parallelogram is a rectangle. In other words: If <D is a right angle and • ABCD is a parallelogram, then <A, <B, and <C are right angles, which means that • ABCD is a rectangle. This is because of the theorem that states interior angles on the same side of the transversal are supplementary and the theorem that states supplementary congruent angles are right angles. 180° Triangle Theorem: The sum of a triangle’s angles is 180. a c b 80 ° 60 ° 150 ° 50° 50 ° 90 ° 30 ° 15 ° All of these triangles’ angles’ sum of measures is 180. 15 ° If a segment is between the midpoints on both sides of a triangle, then that segment is 1) parallel to the base and 2) half as long as the base. a x c In other words: If AX=XE and AY=YB, then XY is parallel to CB and XY=CB. y b This can be proved by using SAS, AIP, Definition of a Parallelogram, and a couple parallelogram theories.