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Geometry Chapter 1 Review Lessons 1.1 – 1.7 TEST Friday, October 25 Homework: Page / , 35 – 44

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Lesson 1.1 Building Blocks of Geometry Point A location in space. No size Line A set of collinear points having no endpoints. No width, only length. Plane A set of points that creates a flat surface that has no depth or edge. Length & width, no height. Collinear Coplanar A set of points that lie on a line. A set of points, segments, lines,… that lie on a plane. A B C A B

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Line Segment Congruent Segments Two or more line segments that are congruent (same size & shape) Midpoint of a Segment A point that divides/bisects a segment into two equal parts. A set of collinear points having two endpoints. X AB Y AB XY A Lesson 1.1 Building Blocks of Geometry

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Ray A XY A Midpoint of a Segment (formula) x 1, y 1 x 2, y 2 B G H Lesson 1.1 Building Blocks of Geometry

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Congruent Angles Two or more angles with the same measure Angle The union of two noncollinear rays having a common endpoint. < AXB X B A X B A S T R AXB RST means that the measure of both angles are equal. Lesson Building Blocks of Geometry

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Angle of Reflection The reflection of an angle will have the same measure from the reflected surface as the initial angle. 50 o Incoming angle = Outgoing angle Lesson Building Blocks of Geometry

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Right Angle Acute Angle Obtuse Angle An angle whose measure is equal 90 o.o. An angle whose measure is > 90 o.o. An angle whose measure is < 90 o.o. Lesson Building Blocks of Geometry

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Complimentary Angles Supplementary Angles Two angles whose sum of measure equals 90°. 1 + 2 = 90°. Two angles whose sum of measure equals 180°. 4 + 5 = Adjacent Complimentary Angles Two angles whose sum of measure equals 90°. 6 + 7 = 90°. 4 5 Lesson Building Blocks of Geometry

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Vertical Angles Linear Pair of Angles Opposite and congruent angles formed by the intersection of two lines. 1 = 2 Two adjacent supplementary angles. 8 + 9 = Lesson Building Blocks of Geometry

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Polygon A closed plane figure formed by the connecting line segments endpoint to endpoint with each segment intersecting exactly two other segments. Triangle A polygon having the fewest possible number of sides. n-gon A polygon with n number of sides where n is equal to any positive integer. Triangle Octagon n = 3n = 8 Lesson Building Blocks of Geometry

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Naming Polygons n= 5Pentagon n= 6 Hexagon n= 8 Octagon Lesson Building Blocks of Geometry

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Polygon Features Consecutive angles Consecutive sides Consecutive vertices A B FAB & ABC F E C D AF & FE F & E Lesson Building Blocks of Geometry

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Diagonal of a Polygon A line segment that connects two nonconsecutive vertices of a polygon. A E F D C B AC. AD, & AE are each diagonals of this polygon. Lesson Building Blocks of Geometry

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Groups of Polygons Equilateral polygon A polygon with all sides equal in length. Equiangular polygon A polygon with all angles equal in measure. Regular polygon A polygon with all angles equal in measure and all sides equal in length. Lesson Building Blocks of Geometry

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Groups of Polygons Equilateral polygon Equiangular polygon Regular polygon The rhombus has all sides congruent. The rectangle has all angles congruent. The square has all angles and sides congruent. Lesson Building Blocks of Geometry

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Right Triangle A triangle with one right angle. Acute Triangle A triangle with three acute angles. Lesson Building Blocks of Geometry

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Obtuse Triangle A triangle with one obtuse angle. Scalene Triangle A triangle with no congruent sides. Lesson Building Blocks of Geometry

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Equilateral Triangle A triangle with all sides congruent. Isosceles Triangle A triangle with two congruent sides. Lesson Building Blocks of Geometry

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Trapezoid A quadrilateral with two sides parallel. Parallelogram A quadrilateral with both pairs of opposites sides parallel and congruent. A C B D AB DC D C BA AC BD Lesson Building Blocks of Geometry

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Kite A quadrilateral with two pair of adjacent sides congruent. Rhombus A quadrilateral with opposite sides parallel and all sides congruent. AB DC AD BC A C B D A BD C AB BC CD DA Lesson Building Blocks of Geometry

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Rectangle A parallelogram with all angle congruent (right angles). Square A parallelogram all angles congruent and all sides congruent. A C B D AB DC AC BD A B D C AB BC CD DA AD BC AB DC AD BC Lesson Building Blocks of Geometry

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Circle – The set of points equidistant to a given point. Radius – A segment with one endpoint on the circle and one endpoint on the center. XA Diameter – A chord that passes thru the center of the circle. EB Chord – A segment whose endpoints lie on the circle. FD Tangent – A line that intersects a circle at only one point. Line GC Arc – The distance between two points on a circle. AB A D C E F B X Lesson Building Blocks of Geometry G

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A D C E F B X Lesson Building Blocks of Geometry J..

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Through any two points there is exactly one line. A · · B Through any three points there is at least one plane and through any three non-collinear points there is exactly one plane.. A B.. C Conjectures

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A B If two lines intersect, then they intersect in exactly one point. l m A Line l intersects line m at A. X Y Conjectures

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1 dimension 3 dimensions 2 dimensions A line contains at least two points A plane contains at least 3 points not in a line Space contains at least four points not all in one plane Dimensions

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