Fall 2012 Geometry Exam Review

1. Fall 2012Geometry Exam Review

2. Chapter 1-5 Review p.200-201

3. Chapter 1-5 Review p.200-201

4. Chapter 1-5 Review p.200-201

5. Chapter 1 • Points, lines, planes • Collinear, coplanar, intersection • Segments, rays, and distance (length) • Distance = |x2-x1| • 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 = s2 • 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.