Unit 1 Unit 1 A M. M.Sigley, Baker MS. Unit 1 Unit 1. 3 M.Sigley, Baker MS

Transcription

1 A M S 1 2 G O E A B 3 4

2 LINE POINT Undefined No thickness Extends infinitely in two directions Designated with two points Named with two capital letters or Undefined No size Named with a capital letter one lower case letter 2 1 SEGMENT PLANE Part of a line Designated by two endpoints Named with two capital letters from the endpoints Undefined Extends infinitely in all directions Designated with three points Named with three capital letters 4 3

3 U V D G E W Z D O 5 6 L C N J D E 7 8

4 COPLANAR COLLINEAR In the same plane Point D is NOT coplanar Points that lie on the same line Any two points are collinear Points U, V, W, and Z are collinear 6 5 ANGLE RAY Made by two rays with a common endpoint called a VERTEX Divides a plane into two regions INTERIOR and EXTERIOR Point N is in the interior of the angle Part of a line that begins at a point and extends infinitely in one direction Named with the endpoint and another point on the ray 8 7

5 D 9 10 B N G E O 11 12

6 POSTULATE POSTULATE The intersection of two planes is a line. The intersection of two lines is exactly one point POSTULATE POSTULATE If two points are in a plane then the line containing them is also in the plane. Through any two points there is exactly one line

7 B N B L N BL + LN C F E O D E m CDF + m FDE S L 15 16

8 POSTULATE Segment Addition: If three points are on the same line, then the lengths of the smaller segments added together will equal the length of the larger segment. BL + LN = BN The distance between two points (length of a segment) is b - n. (absolute value of difference of the number line coordinates) POSTULATE Complementary Angles: Two angles that when added together have a total measure of 90. Angle Addition: The measure of two angles sharing a common side can be added together. m CDF + m FDE = m CDE 16 15

9 E O E L S S L

10 Right Angle: An angle with a measure of 90. Supplementary Angles: Two angles that when added together have a measure of Obtuse Angle: An angle with a measure that is between 90 and 180. Acute Angle: An angle with a measure of less than

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12 Perpendicular Lines: Two lines that intersect to form a right angle. Parallel Lines: Two lines in the same plane that never intersect Angle Bisector: An angle with a measure that is between 90 and 180. Segment Bisector: A line that intersects a segment at its midpoint dividing it into two congruent pieces

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14 Circumscribed Circle: Outside triangle touches all vertices Center of circle called the circumcenter and is equidistant from vertices Constructed from perpendicular bisectors Inscribed Circle: Inside triangle touches all sides Center of circle called the incenter and is equidistant from sides of triangle Constructed from angle bisectors Orthocenter: The intersection of the altitudes of a triangle. Altitude: A perpendicular line segment that connects the vertex of a triangle with the opposite side

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16 Centroid: The intersection of the medians of a triangle. Median: A line segment that connects the vertex of a triangle to the midpoint of the opposite side Rotation: Transformation Turn Maintains same size and shape Translation: Transformation Slide Stays the same size and shape 32 31

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18 Reflection: Transformation Flip Maintains same size and shape