Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Fall 2011 Exam Review
Document related concepts
Plane of rotation wikipedia , lookup
Technical drawing wikipedia , lookup
Projective plane wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Multilateration wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Transcript
Fall 2012 Geometry Exam Review Chapter 1-5 Review p.200-201 Problems Answers 1 One 2 a. Yes, skew b. No 3 If you enjoy winter weather, then you are a member of the skiing club. 4 -1 5 Transitive Property 6 180 7 180 8 5 9 <1 10 Segment EB 11 Bisects, β₯ 12 a. A and B Chapter 1-5 Review p.200-201 Problems Answers 13 a. βΏπ ππ΄ b. π ππππππ‘ π·π΅ c. m<E 14 171 15 150, 150 16 15, 15, 16 17 3r - s 18 Median 19 Angle Bisector 20 Isosceles 21 72, 36 22 Isosceles 23 <ABC, <BAC, <ACD, and <CFD 24 m>1=m>4=30; m<2=m<3=15 Chapter 1-5 Review p.200-201 Problems Answers 25 m<1=m<4=k, m<2=m<3= 45-k 26 Parallelogram 27 <NOM, <LMO, <NMO 28 Midpoint, segment MN 29 PQ + ON Chapter 1 ο Points, lines, planes ο Collinear, coplanar, intersection ο Segments, rays, and distance (length) ο‘ Distance = |x2-x1| ο Congruent segments have ___________ ο The segment midpoint divides the segment __________ ο A segment bisector intersects a segment at _____ Chapter 1- Angles ο Sides and vertex ο Acute, obtuse, right, straight (measure = ?) ο Adjacent angles ο‘ Have a common vertex and side but share no interior points ο Angle bisector Chapter 1 Postulates and Theorems ο Segment Addition Postulateο‘ If B is between A and C, then AB + BC = AC ο Angle Addition Postulate ο‘ m<AOB +m<BOC = m<AOC ο‘ If <AOC is a straight angle, and B is not on line AC, then m<AOB +m<BOC = 180 Chapter 1 ο A line contains at least _____ point(s). ο‘ two ο A plane contains at least _______ point(s) not in one line. ο‘ three ο Space contains at least _____ points not all in one plane. ο‘ four ο Through any three non-collinear points there is exactly ________. ο‘ one plane Chapter 1- p. 23 ο If two planes intersect, their intersection is a _____ ο‘ line ο If two lines intersect, they intersect in _______ ο‘ exactly one point ο Through a line and a point not on the line, there is ο‘ exactly one plane ο If two lines intersect, then _______ contains the lines ο‘ exactly one plane Properties from Algebra p.37 ο Properties of Equality ο‘ ο‘ ο‘ Addition, Subtraction, Multiplication, Division Substitution Reflexive ο· ο‘ Symmetric ο· ο‘ ο‘ (a=a) (if a=b, then b=a) Transitive Distributive ο Properties of Congruence ο‘ ο‘ ο‘ Reflexive Symmetric Transitive Chapter 2 ο Midpoint Theorem p.43 ο Angle Bisector Theorem p.44 ο Complementary and supplementary angles p. 61 ο Vertical angles ο Definition of Perpendicular lines p.56 ο‘ Two lines that intersect to form right angles ο If two lines are perpendicular they form _______ ο‘ Congruent adjacent angles ο If two lines form congruent adjacent angles, then the two lines are______________ ο‘ Perpendicular Chapter 2 ο If the exterior sides of two adjacent acute angles are perpendicular, then the angles are ______ ο‘ complementary ο If two angles are supplements (complements) of congruent angles (or of the same angle), then the two angles are _____________ ο‘ congruent Chapter 3- Parallel Lines and Planes ο Parallel lines ο‘ Coplanar lines that do not intersect ο Skew lines ο‘ Non-coplanar lines that do not intersect and are not parallel ο Parallel planes ο‘ Planes that do not intersect ο If two parallel planes are cut by a third plane, the lines of intersection are ________ ο‘ Parallel (think of the ceiling and floor and a wall) Chapter 3 ο Transversal ο Alternate interior angles ο Same-side interior angles ο Corresponding angles ο If 2 parallel lines are cut by a transversal, which sets of angles are congruent? Which are supplementary? ο If a transversal is perpendicular to one of two parallel lines, it is __________ ο‘ Perpendicular to the other one also ο Ways to prove two lines are parallel ο‘ Show a pair of corresponding angles are congruent ο‘ Show a pair of alternate interior angles are congruent ο‘ Show a pair of same-side interior angles are supplementary ο‘ In a plane, show both lines are perpendicular to a third line ο‘ Show both lines are parallel to a third line Chapter 3- Classification of Triangles ο Scalene, isosceles, and equilateral ο Acute, obtuse, right, and equiangular ο Sum of the measures of the angles in a triangle = ? ο Corollaries on p.94 Chapter 3- Polygons ο Polygon- βmany anglesβ ο Sum of the interior angles of a convex polygon with n sides = ? ο‘ (n-2)180 ο Measure of each interior angle of a convex polygon with n sides = ? ο‘ (n-2)180/n ο Sum of the measures of the exterior angles of any convex polygon = ? ο‘ 360 ο Measure of each exterior angle of a regular convex polygon= ? ο‘ 360/n Chapter 4 ο Congruent figures have the ο‘ Same size and shape ο‘ Corresponding sides and angles are congruent ο Naming congruent triangles ο CPCTC ο SAS, SSS, ASA, AAS ο HL, HA, LL, LA ο Isosceles Triangle Theorem and its Converse Chapter 4 Corollary: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. ο Equilateral and equiangular triangles ο Altitudes, medians, and perpendicular bisectors ο If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. ο If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle. ο Distance from a point to a line Chapter 5- Definitions and Properties ο Properties of Parallelograms ο Parallelograms ο‘ Rectangle ο‘ Rhombus ο‘ Square ο Trapezoids ο‘ Median= ½ (b1 + b2) ο Isosceles Trapezoids ο‘ Base angles are congruent ο Triangles ο‘ Segment joining the midpoints of 2 sides ο‘ Segment through the midpoint of one side and parallel to another side Chapter 5 ο The midpoint of the hypotenuse of a right triangle is equidistant from the 3 vertices. ο If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle. ο‘ ο‘ ο‘ 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. ο If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. ο‘ ο‘ Pairs of opposite sides in a are congruent Therefore all sides must be congruent Chapter 11-Area ο Parallelograms ο‘ A= b*h ο‘ Rectangle ο· ο‘ Rhombus ο· ο‘ A = b*h A= ½ d1 * d2 Square ο· A = s2 ο Trapezoids ο‘ ½ (b1 + b2)*h ο Triangles ο‘ A= ½ b*h ο The area of a region is the sum of the areas of its non- overlapping parts.
