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# Geometry

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### Geometry - Page Text Content

BC: "Don't cry because it's over, Smile because it happened." - Dr Seuss

FC: Geometry Book by Katie Huddleston 2nd period 12/07/11

1: Table of Contents | pg. 2&3----- Chapter 1 Basic Geometry pg. 4&5----- Angles& Their Measures pg 6&7----- Chapter 2 Segments and Angles pg. 8&9----- Supplementary, Complementary& Vertical Angles pg. 10-11----- Chapter 3 Parallel lines & Transversal pg. 12-13--Perpendicular Lines pg. 14-15-----Chapter 4 Triangle Relationships pg. 16-17----- Pythagorean Theorem& Distance Formula pg. 18-19----- Chapter 5 Congruent Triangles pg.20-21----- Polygons | 1

2: Basic Geometry | plane: has 2 dimensions | Postulate 1 Two points Determine a Line: through any two points there is exactly one line a line: has 1 dimension | Postulate 2 Three points Determine a Plane: through any three points not on a line there is exactly one plane | Postulate 3 Intersection of Two Lines: if two lines intersect, then their intersection is a point | Postulate 4 Intersection of Two Planes: if two planes intersect, then their intersection is a line | 2

3: a ray like AB | 3

4: congruent segments are segments with the same length | 90 degrees | 180 degrees | less than 90 degrees | more than 90 degrees | Angles and Their Measures | 4

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6: Segments and Angles | Segment Bisector: a segment, ray, line, or plane that intersects a segment at its midpoint | angle bisector: a ray that divides an angle into two angles that are congruent | 6

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8: complementary angles: the sum two angles is 90 degrees | supplementary angles: the sum of two angles is 180 degrees | Vertical angles: two angles that aren't adjacent and their sides are formed by two two intersecting lines | Theorem 2.3 Vertical Angles Theorem: vertical angles are congruent | Supplementary, Complementary, and Vertical Angles | 8

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10: Parallel Lines and transversal | parallel lines: on the same plane but don't intersect | Transversal: a line that intersects two or more coplanar lines at different points | Corresponding Angles: two angles that occupy corresponding positions Alternate Interior Angles: two angles that lie b/t two lines on opposite sides of the transversal Alternate Exterior Angles: two angles that lie outside two lines opposite sides of the transversal Same-Side Interior Angles: two angles that lie b/t two lines on the same side of the transversal | 10

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12: Perpendicular Lines | perpendicular lines: two lines intersect to form a right angle(s) | 12

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14: Triangle Relationships | triangle: a figure formed by 3 segments joining 3 non-collinear points | Theorem 4.1 Triangle Sum Theorem: the sum of the measures of the angles of a triangle is 180 degrees | Corollary to the Triangle Sum Theorem: the acute angles of a right triangle are complementary | 14

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16: Pythagorean Theorem and Distance Formula | Theorem 4.7 The Pythagorean theorem: in a right triangular, the square of the length of the hypothesis is equal to the sum of the squares of the lengths of the legs | the distance formula: | Theorem 4.8 the converse of the Pythagorean theorem: if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other 2 sides, then the triangle is a right triangle | 16

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18: Congruent Triangles | Postulate 12 side-side-side congruence postulate: if 3 sides of 1 triangle are congruent to 3 sides of a second triangle, then the 2 triangles are congruent | Postulate 13 side-angle-side congruence postulate: if 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of a second triangle, then the 2 triangles are congruent | Postulate 14 angle-side-angle congruence postulate: if 2 angles & the included side of 1 triangle are congruent to 2 angles and the included side of a second triangle, then the 2 triangles are congruent | theorem 5.1 angle-angle-side congruence theorem: if 2 angles & a non-included side of 1 triangle are congruent to 2 angles and the corresponding non-included side of a second triangle, then the 2 triangles are congruent | 18 | Theorem 5.2 Hypotenuse-Leg Theorem: if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the 2 triangles are congruent

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20: Polygons | 20 | polygon: a plane figure that is formed by 3 or more segments | parallelogram: a quadrilateral with both pairs of opposite sides parallel | square: a parallelogram with four congruent sides and four right angles | rhombus:a parallelogram with four congruent sides | rectangle: a parallelogram with four right angles

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