Term Definition Figure

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1 Geometry Unit 1 Packet - Language of Geometry Name: #: Video Notes LT Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruent, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do not have to be able to see the line, it just needs to be possible to draw one) plane an undefined term thought of as a flat surface extending infinitely along its edges. coplanar on the same plane congruent bisect midpoint between angle vertex of an angle identical in shape and size to divide into two congruent pieces the point on a line that is equidistant from both endpoints. The midpoint bisects the segment. a point is between two other points if it lies on a segment that could be drawn from one point to the other two noncollinear rays having a common endpoint the point of intersection of the two rays that form an angle see figures for midpoint and angle bisector 1

2 congruent angles angles with the same measure angle bisector counterexample a ray that has its endpoint at the vertex of the angle and divides the angle into two congruent angles an example that shows a conjecture to be incorrect or a definition to be inadequate Conjecture: All rectangles are squares. Counterexample: Name Wording Figure Segment Addition Postulate If A, B, and C are collinear and B is between A and C, then AB + BC = AC Angle Addition Postulate If R lies in the interior of STV, then m ST R + m RT V = m ST V * Quizlet and flashcards are linked on the class website to use as a resources, or feel free to make your own flashcards to help get these terms down! * 2

3 Video/Small Group Instruction Notes LT Identify and name segments, lines, and rays. Geometry uses precise definitions, postulates, theorems, and notation. It is important that you pay attention to detail to be as successful as possible in this class. The following notations all mean something different: AB AB BA A B AB One thing to note though is that they all use capital letters. Why? In geometry, capital letters are used to denote points and lower case letters are used for other purposes, as you will see. So, what do these mean? A: point A AB : the line segment with endpoints A and B. This could also be written BA AB : the ray with endpoint A that passes through point B BA : the ray with endpoint B that passes through point A A B : the line that passes through points A and B. The line below could have several legitimate names. AB : the distance between point A and point B 3

4 1.1 and 1.2 Review Geometry For problems 1-8, draw the figure that is being described and, where possible, write the appropriate notation. 1) Line AB parallel to ray MN. 2) Collinear points M, N, and Y Figure: Figure: Notation: Notation: 3) Ray HM bisects angle YHR 4) Ray MN bisects segment RT Figure: Figure: Notation: Notation: 5) Ray HM is perpendicular to line RT 6) Line TY bisects and is perpendicular to segment AB. Figure: Figure: Notation: Notation: 7) W is the midpoint of segment TR. 8) Ray GT is parallel to segment MN. Figure: Figure: Notation: Notation: Check answers on website - ask? s if you have any! Then, come up for check-up when you re ready! 4

5 Video/Small Group Instruction Notes LT Classify circles and their parts (radius, chord, diameter, tangent, arc and measure, central angle) Naming a circle: a circle is named using the point at its center. So, P is at right. Vocabulary with circles Chord Diameter Tangent Congruent circles Arc Concentric circles Semicircle Minor arc Major arc Central angle Arc measure 5

6 1.3 Review Geometry For problems 1 8, use the diagram at right. F is the center of the circle. 1) Name a chord. 2) Name a diameter. 3 Name a radius. 4) Name a minor arc. 5) Name a semicircle. 6) Name a major arc. 7) Name a tangent. 8) Name a secant. For problems 9-14, draw a circle that includes the indicated part. 9) central angle MHG 10) major arc AGB 11) secant HB 12) inscribed angle MJT 13) semicircle TGU 14) chord BG 6

7 Check answers on website - ask? s if you have any! Then, come up for 1.3 check-up when you re ready! Additional Information Classify special angle pairs (vertical, linear, complementary, supplementary) and angles (right, acute, obtuse, congruent). Angles Parts of an angle: sides: vertex: Naming angles: Types of angles: Measuring an angle: Now, measure these angles: 7

8 Angle Pairs Complementary Angles Supplementary Angles Vertical Pair of Angles Linear Pair of Angles Classify triangles (right, acute, obtuse, scalene, equilateral, isosceles) Types of triangles : Acute triangle Right triangle Obtuse triangle Scalene Triangle Isosceles Triangle Equilateral triangle 8

9 Classify polygons and their parts (side, vertex, diagonal, convex/concave, congruency, equiangular, equilateral, regular) Polygons diagonal of a polygon a line segment that connects two nonconsecutive vertices perimeter of a polygon the sum of the lengths of its sides equilateral polygon a polygon in which all sides have equal length equiangular polygon a polygon in which all angles have equal measure regular polygon a polygon that is both equilateral and equiangular Convex vs. concave polygons Convex no diagonal is outside the polygon Concave at least one diagonal is outside the polygon 9