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Transcript
February 14, 2015 Get a ruler and your notebook and set it up! Unit 8: Triangle Geometry Pages Title Vocabulary Classifying Triangles Transversals Proof Structure Basic Triangle Proofs Congruent Triangles Congruent Triangles Proofs Vocabulary Reflexive Property: a segment or angle is congruent to itself. Congruent : two angles, segments, or figures are congruent if their measures are equal. Midpoint: results in two segments being congruent. Segment Bisector: a line that intersects a segment and cuts it into two congruent parts. February 14, 2015 Vocabulary Perpendicular Bisector: a line that intersects a segment and cuts it into two congruent parts and two right angles. Angle Bisector: a line (or part of a line) that divides an angle into two congruent parts. Vertical Angles: a pair of congruent opposite angles formed by two intersecting lines. Vocabulary 3rd Angle Theorem: If 2 angles of a triangle are congruent to two angles of another triangle, then the 3rd angles are also congruent. Median: a segment that goes from a vertex to the midpoint of the opposite side. February 14, 2015 Vocabulary Altitude: a segment that goes from the vertex to the opposite side of a triangle and is perpendicular to the other side. Midsegment: a segment which connects the midpoints of two sides of a triangle. Properties -parallel to the side of the triangle it does not intersect. -it is half the length of that same side. Vocabulary Substitution Postulate: if two things are congruent to the same thing then they are congruent to each other. Addition Postulate: if you add the same thing to two equal things then the result is equal. Subtraction Postulate: if you subtract the same thing from two equal things then the result is equal. February 14, 2015 Classifying Triangles By Sides: Scalene Triangle: no congruent sides. Isosceles Triangle: two sides and angles are congruent. Equilateral Triangle: three congruent sides and angles. (Equiangular) Classifying Triangles By Angles: Acute Triangle: all angles measurements less than 90o. Obtuse Triangle: one angle greater than 90o. Right Triangle: a 90 angleo. February 14, 2015 Quadrilaterals Parallelogram: Quadrilateral with two pairs of parallel sides. Rectangle: Quadrilateral where all four angles are right angles. Square: Quadrilateral where all four sides are of equal length, and all four angles are right angles. Rhombus: Quadrilateral where all four sides are of equal length. Kite: Quadrilateral where two pairs of adjacent sides are of equal length. Trapezoid: Quadrilateral where at least one pair of opposite sides are parallel. Square: Quadrilateral where all four sides are of equal length, and all four angles are right angles. Properties -The diagonals of the shape are congruent. -The diagonals of the shape bisect each other at right angles. -Two pairs of parallel sides. February 14, 2015 Rectangle: Quadrilateral where all four angles are right angles. Properties -The diagonals bisect each other. -Opposite sides are congruent. Parallelogram: Quadrilateral with two pairs of parallel sides. Properties -Diagonals are not always congruent. -Opposite sides are parallel. -Opposite angles are congruent February 14, 2015 Rhombus: Quadrilateral where all four sides are of equal length. Properties -The diagonals bisect each other. -Opposite sides are parallel. -Opposite angles are congruent. Kite: Quadrilateral where two pairs of adjacent sides are of equal length. Properties -One diagonal is bisected. -Diagonals intersect at right angles. February 14, 2015 Trapezoid: Quadrilateral where at least one pair of opposite sides are parallel. Isosceles Trapezoid -legs are congruent -diagonals are congruent -common base angles are congruent. Transversals Transversal: a line that intersects two or more coplanar lines at different points. 11-20 Pg February 14, 2015 Transversals 1 3 5 7 2 11-20 Pg 4 6 8 Corresponding Angles: , angles that occupy the same position relative to the transversal and the two lines. Alternate Interior Angles: angles that are inside of the two lines and on opposite sides of the transversal. Transversals 1 3 5 7 2 4 6 8 Alternate Exterior Angles: angles that are outside of the two lines and on opposite sides of the transversal. Same Side Interior Angles: angles that lie between the two lines and on the same side of the transversal. Same Side Exterior Angles: angles that lie outside of the two lines and on the same side of the transversal. 11-20 Pg February 14, 2015 11-20 Pg Transversals Ex 1: 140o Ex 2: 40o 120o 11-20 Pg Transversals Ex 3: 2x + 20 x + 10 3x+15 8x-20 February 14, 2015