Geometry

1. Geometry Chapter 1 Review Lessons 1.1 – 1.7 TEST Friday, October 25 Homework: Page 90 - 92/ 1 - 32, 35 – 44

2. 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. A set of points that creates a flat surface that has no depth or edge. Length & width, no height. Plane Collinear C A B • • • A set of points that lie on a line. A • Coplanar A set of points, segments, lines,… that lie on a plane. B •

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

4. G A A X Y Lesson 1.1 Building Blocks of Geometry • Midpoint of a Segment (formula) x 1, y1 x 2, y2 B Ray • • H

5. R A A S X X T B B Lesson 1.1 - Building Blocks of Geometry Angle The union of two noncollinear rays having a common endpoint. < AXB • • • Congruent Angles Two or more angles with the same measure • • AXB  RST means that the measure of both angles are equal. •

6. Lesson 1.1 - Building Blocks of Geometry Angle of Reflection The reflection of an angle will have the same measure from the reflected surface as the initial angle. 50o Incoming angle = Outgoing angle 50o

7. Lesson 1.1 - Building Blocks of Geometry An angle whose measure is equal 90 o. Right Angle Acute Angle An angle whose measure is < 90 o. Obtuse Angle An angle whose measure is > 90 o.

8. Lesson 1.1 - Building Blocks of Geometry Complimentary Angles Two angles whose sum of measure equals 90°. 1 +  2 = 90°. 1 6 2 7 Two angles whose sum of measure equals 90°. 6 +  7 = 90°. Adjacent Complimentary Angles Two angles whose sum of measure equals 180°.  4 +  5 = 180°. Supplementary Angles 4 5

9. Lesson 1.1 - Building Blocks of Geometry Vertical Angles Opposite and congruent angles formed by the intersection of two lines.  1 =  2 1 2 Linear Pair of Angles Two adjacent supplementary angles .  8 +  9 = 180. 8 9

10. Lesson 1.1 - Building Blocks of Geometry Polygon A closed plane figure formed by the connecting line segments endpoint to endpoint with each segment intersecting exactly two other segments. A polygon having the fewest possible number of sides. Triangle n-gon A polygon with n number of sides where n is equal to any positive integer. Octagon Triangle n = 3 n = 8

11. Lesson 1.1 - Building Blocks of Geometry Naming Polygons n= 5 Pentagon Hexagon n= 6 Octagon n= 8

12. A B C F E D AF & FE Lesson 1.1 - Building Blocks of Geometry Polygon Features Consecutive angles FAB & ABC Consecutive sides Consecutive vertices F & E

13. A B F C E D Lesson 1.1 - Building Blocks of Geometry Diagonal of a Polygon A line segment that connects two nonconsecutive vertices of a polygon. AC. AD, & AE are each diagonals of this polygon.

14. Lesson 1.1 - Building Blocks of Geometry Groups of Polygons A polygon with all sides equal in length. Equilateral polygon A polygon with all angles equal in measure. Equiangular polygon A polygon with all angles equal in measure and all sides equal in length. Regular polygon

15. Lesson 1.1 - Building Blocks of Geometry Groups of Polygons Equilateral polygon The rhombus has all sides congruent. The rectangle has all angles congruent. Equiangular polygon The square has all angles and sides congruent. Regular polygon

16. Lesson 1.1 - Building Blocks of Geometry Right Triangle A triangle with one right angle. Acute Triangle A triangle with three acute angles.

17. Lesson 1.1 - Building Blocks of Geometry Obtuse Triangle A triangle with one obtuse angle. Scalene Triangle A triangle with no congruent sides.

18. Lesson 1.1 - Building Blocks of Geometry Equilateral Triangle A triangle with all sides congruent. Isosceles Triangle A triangle with two congruent sides.

19. AB DC A B AB DC C AC BD D Lesson 1.1 - Building Blocks of Geometry Trapezoid A quadrilateral with two sides parallel. B A C D A quadrilateral with both pairs of opposites sides parallel and congruent. Parallelogram

20. A D B C AB DC AB  BC  CD  DA AD BC Lesson 1.1 - Building Blocks of Geometry Kite A quadrilateral with two pair of adjacent sides congruent. A quadrilateral with opposite sides parallel and all sides congruent. Rhombus A D B C

21. AB  DC AD BC AD  BC AB DC AB DC AB  BC  CD  DA AC BD Lesson 1.1 - Building Blocks of Geometry Rectangle A parallelogram with all angle congruent (right angles). A B D C A parallelogram all angles congruent and all sides congruent. Square A B D C

22. Lesson 1.1 - Building Blocks of Geometry • 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 F B E X D C G

23. Lesson 1.1 - Building Blocks of Geometry . . A J F B E X D C

24. Conjectures • 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

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

26. 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 1 dimension 2 dimensions 3 dimensions