1. Fall 2012 Geometry Exam Review

2. Chapter 1-5 Review p.200-201 ProblemsAnswers 1One 2a.Yes, skew b.No 3If you enjoy winter weather, then you are a member of the skiing club. 4 5Transitive Property 6180 7 85 9<1 10Segment EB 11 12a.A and B b.Ray SR and ray ST

3. Chapter 1-5 Review p.200-201 ProblemsAnswers 13 14171 15150, 150 1615, 15, 16 173r - s 18Median 19Angle Bisector 20Isosceles 2172, 36 22Isosceles 23<ABC, <BAC, <ACD, and <CFD 24m>1=m>4=30; m<2=m<3=15

4. Chapter 1-5 Review p.200-201 ProblemsAnswers 25m<1=m<4=k, m<2=m<3= 45-k 26Parallelogram 27<NOM, <LMO, <NMO 28Midpoint, segment MN 29PQ + ON

5. Chapter 1 Points, lines, planes Collinear, coplanar, intersection Segments, rays, and distance (length)  Distance = |x 2 -x 1 | Congruent segments have ___________ The segment midpoint divides the segment __________ A segment bisector intersects a segment at _____

6. Chapter 1- Angles Sides and vertex Acute, obtuse, right, straight (measure = ?) Adjacent angles  Have a common vertex and side but share no interior points Angle bisector

7. Chapter 1 Postulates and Theorems Segment Addition Postulate-  If B is between A and C, then AB + BC = AC Angle Addition Postulate  m<AOB +m<BOC = m<AOC  If <AOC is a straight angle, and B is not on line AC, then m<AOB +m<BOC = 180

8. Chapter 1 A line contains at least _____ point(s).  two A plane contains at least _______ point(s) not in one line.  three Space contains at least _____ points not all in one plane.  four Through any three non-collinear points there is exactly ________.  one plane

9. Chapter 1- p. 23 If two planes intersect, their intersection is a _____  line If two lines intersect, they intersect in _______  exactly one point Through a line and a point not on the line, there is  exactly one plane If two lines intersect, then _______ contains the lines  exactly one plane

10. Properties from Algebra p.37 Properties of Equality  Addition, Subtraction, Multiplication, Division  Substitution  Reflexive  (a=a)  Symmetric  (if a=b, then b=a)  Transitive  Distributive Properties of Congruence  Reflexive  Symmetric  Transitive

11. Chapter 2 Midpoint Theorem p.43 Angle Bisector Theorem p.44 Complementary and supplementary angles p. 61 Vertical angles Definition of Perpendicular lines p.56  Two lines that intersect to form right angles If two lines are perpendicular they form _______  Congruent adjacent angles If two lines form congruent adjacent angles, then the two lines are______________  Perpendicular

12. Chapter 2 If the exterior sides of two adjacent acute angles are perpendicular, then the angles are ______  complementary If two angles are supplements (complements) of congruent angles (or of the same angle), then the two angles are _____________  congruent

13. Chapter 3- Parallel Lines and Planes Parallel lines  Coplanar lines that do not intersect Skew lines  Non-coplanar lines that do not intersect and are not parallel Parallel planes  Planes that do not intersect If two parallel planes are cut by a third plane, the lines of intersection are ________  Parallel (think of the ceiling and floor and a wall)

14. Chapter 3 Transversal Alternate interior angles Same-side interior angles Corresponding angles If 2 parallel lines are cut by a transversal, which sets of angles are congruent? Which are supplementary? If a transversal is perpendicular to one of two parallel lines, it is __________  Perpendicular to the other one also

15. Ways to prove two lines are parallel  Show a pair of corresponding angles are congruent  Show a pair of alternate interior angles are congruent  Show a pair of same-side interior angles are supplementary  In a plane, show both lines are perpendicular to a third line  Show both lines are parallel to a third line

16. Chapter 3- Classification of Triangles Scalene, isosceles, and equilateral Acute, obtuse, right, and equiangular Sum of the measures of the angles in a triangle = ? Corollaries on p.94

17. Chapter 3- Polygons Polygon- “many angles” Sum of the interior angles of a convex polygon with n sides = ?  (n-2)180 Measure of each interior angle of a convex polygon with n sides = ?  (n-2)180/n Sum of the measures of the exterior angles of any convex polygon = ?  360 Measure of each exterior angle of a regular convex polygon= ?  360/n

18. Chapter 4 Congruent figures have the  Same size and shape  Corresponding sides and angles are congruent Naming congruent triangles CPCTC SAS, SSS, ASA, AAS HL, HA, LL, LA Isosceles Triangle Theorem and its Converse

19. Chapter 4 Corollary: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Equilateral and equiangular triangles Altitudes, medians, and perpendicular bisectors If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle. Distance from a point to a line

20. Chapter 5- Definitions and Properties Properties of Parallelograms Parallelograms  Rectangle  Rhombus  Square Trapezoids  Median= ½ (b1 + b2) Isosceles Trapezoids  Base angles are congruent Triangles  Segment joining the midpoints of 2 sides  Segment through the midpoint of one side and parallel to another side

21. Chapter 5 The midpoint of the hypotenuse of a right triangle is equidistant from the 3 vertices. If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle.  Pairs of opposite angles of a are congruent  Measure of 4 interior angles of a add up to 360.  Therefore all angles are right angles. If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.  Pairs of opposite sides in a are congruent  Therefore all sides must be congruent

22. Chapter 11-Area Parallelograms  A= b*h  Rectangle  A = b*h  Rhombus  A= ½ d1 * d2  Square  A = s 2 Trapezoids  ½ (b1 + b2)*h Triangles  A= ½ b*h The area of a region is the sum of the areas of its non- overlapping parts.