**Honors Geometry**
**Chapter 1 & 2 Syllabus**
**Section 1.1 Terminology**
terms: undefined terms - point, line, plane
definitions - geometry, deductive reasoning, postulates, theorems
Review existing knowledge of geometric terms
hw: pp. 4-5
**Section 1.2 Patterns**
Review solving quadratic equations using examples
Use of the Pythagorean theorem (“rope stretchers”)
define: irrational/ rational number, inductive reasoning, generalization
hw: pp. 9-12, read about Euclid - We are studying “Euclidean geometry”
**Section 2.1 Logic**
define: sets, elements, contain, subset, union, intersection, logic, the null set (danish letter Ø)
pp 18-20 (focus on #9)
**Section 2.2** **Algebraic Background info.**
define: natural numbers, whole numbers, counting numbers, rational numbers, irrational numbers, one-to-one correspondence
memorize properties of equality/ inequality
memorize all other fundamental algebraic properties
review order of operations (“__P__lease __e__xcuse __m__y __d__ear __A__unt __S__ally”)
pp. 25 - 26
**Section 2.3 Distance**
define: absolute value (arithmetic, algebraic, and geometric)
Note: absolute value(sum) ≠ sum(absolute value)
p.28
**Section 2.4 Distance (continued) **
define: measure
memorize __distance postulate__ (how to organize postulates and theorems)
Use ruler/ tape measure
p. 30 #1,10
**Section 2.5 Distance (continued)**
review one-to-one correspondence
memorize the __ruler postulate__
memorize the __ruler placement postulate __- “it’s O.K. to move the ruler”
discuss various coordinate systems
pp. 35-36 #3 - 6,8
**Section 2.6 Mathematical Definitions **
note: Watch notation...
define mathematically: between, determine, contain, segment, endpoints, length, ray, opposite rays, midpoint, bisect
memorize: __line postulate __(Euclidean geometry)
__point plotting theorem__(note: on a **ray**)
pp. 42 - 43
**Test** - Chapter 1 and 2
(approximately 7-8 days)
**Honors Geometry**
**Chapter 3 Syllabus**
**Section 3.1 Adding the third dimension - “perspective”**
define: edge, lateral face, base
pp. 51-52
**Section 3.2 Properties of Lines/Planes**
pay special attention to “__queries” and “notes”__
review point, line, and plane
define: collinear, coplanar
memorize __line postulate__
memorize __plane- space postulate__
pp.54-56 #1-18
**Section 3.3 More** **Properties of Lines/Planes**
Differentiate between metric (or measuring) properties
incidence properties (occurence)
Do this section inductively
memorize: __flat plane postulate__
__ plane postulate__
__ intersection of planes postulate__
List definitions,theorems, postulates in a central location!!
(If computerized on a database, consider having one field for name, one for goal of theorem, one for ordered numbers)
pp. 59-61 except #19
**Section 3.4 Separation Postulates (regions)**
define: convex (inductively), half-plane, half-space
What would a __Line Separation Postulate__ state?
Paraphrase the Plane Separation Postulate.
note: answer query on p. 64
pp. 65-67 except #15-16
**Section 3.5 Topology (extension)**
mobius strip, Bridges of Koenigsberg
time to analyze problems individually before giving certain properties of topology. Consider other discrete topics such as Euler and Hamiltonian Circuits...(Reports?)
**Chapter Review**
**Chapter Test **
**Honors Geometry**
**Chapter 4 Syllabus**
preparation - define interior of an angle on your own.
define interior of a triangle on your own.
**Section 4.1 Angles and Triangles **
define: angle (watch notation), triangles, interior of a triangle,
exterior of a triangle
pp. 81-83 all
**Section 4.2 Comparison of Angle Measurement to Segment Measurement**
define: linear pair, supplementary
measuring angles (watch notation) in degrees, radians, or gradients, mils
memorize: the angle measurement postulate
angle construction postulate
angle addition postulate
supplement postulate
determine a one to one correspondence between metric postulates for angles and those for segments
pp. 87-90 #1-6,8,11-21 (day 1) #22 - 25 (day 2)
**Section 4.3 Coterminal Angles**
discuss briefly
**Section 4.4 Angle Definitions**
define: right/obtuse/acute angles
congruent/complementary/ supplementary angles
perpendicular lines
Begin to organize your postulates, definitions in your notebooks
on your computer
pp. 96-97 all
**Section 4.5 Equivalence Relations**
Is congruence for segments an equivalence relation?...
Satisfy properties...
a) transitive postulate (*remember: these are properties of *
b) reflexive postulate *numbers*)
c) symmetric postulate
pp. 98-100 (“wanna be proofs”)
**Section 4.6 Angle Theorems**
define: properties of complements, supplements
Explain why each theorem must be true...
4.2 - 4.5 intuitively based on definitions
4.6 - 4.8 thorough 2 column proof (memorize the logic)
pp.103 - 104 all
**Section 4.7 Angle Theorems (continued)**
Prove these while books are not open
pp. 106-108 all
**Section 4.8 Conditional Statements (form)**
define: hypothesis, conclusion
note: In any definition using the word “if”, the hypothesis and the conclusion are reversible (a biconditional statement)
p. 109
and preparation for section 4.9
**Section 4.9 Proof!!**
For each assertion there must be support.Support comes from???
This section includes a detailed review of many postulates and theorems preceding this section.
Problem Solving!
hand out notes on analyzing proofs
pp.112-117 #1 - 18 all (group work)
**Chapter Review ** pp. 117-
**Honors Geometry**
**Chapter 5 Syllabus**
**Section 5.1 Correspondence**
Identify corresponding parts (those which can be superimposed on each other) of two figures. When listing a congruence be sure these are in order. -- Use overheads
define: congruence, identity
hw: pp. 126-128 # 1-11 except #9
**Section 5.2 Congruence**
“ = “ real numbers are being compared
“ = “ segments, angles, and triangles are being compared
define:included side or angle
show congruence is an equivalence relation
hw: pp. 133-135 #1-10,12-14
Preparation for section 5.3 (**on sketchpad**)
**Section 5.3 Congruence Postulates - **
treat these as postulates - accept quickly and utilize them...
hw: pp.139 - 140 all
**Section 5.4 Proof (do-it-yourself)**
analyze methodology in detail
notes on abbreviating reasons
hw:pp.143-146 more practice (Use your “hints” page)
**Section 5.5 more practice on Proofs**
hw:pp.149-151 except #25
**Section 5.6 Angle Bisector Theorem **(Application of Congruence)
define: existence (incidence) theorems
uniqueness theorems
Application of congruent triangles
Show how constructions may be a useful tool in analyzing a proof
hw: pp.153-154 concentrate on #7-9
**Section 5.7 Isosceles and Equilateral Triangles**
Application of congruent triangles
define: isosceles, base, base angles, legs, vertex angle, equiangular, equilateral, scalene, corollary
Look at proof of isosceles triangle theorem very carefully
hw: pp.157-158
**Section 5.8 Converses**
define: converse, conditional, biconditional
How to use the phrase “if and only if” to your benefit
note: All definitions can be rewritten as biconditional statements!
hw: pp. 160-161
**Section 5.9 Overlapping Triangles**
The key is to make them non- overlapping so that they are very similar to every other proof you’ve experienced.
group work
hw: pp. 164-166 all (on overheads)
**Section 5.10 Quadrilaterals, Medians, and Bisectors**
define: quadrilateral, diagonal, rectangle, square, median
Differentiate between an angle bisector and the angle bisector of a triangle.
hw: pp. 168-169 #1-12,14
Review for test - do supplementary problems if you wish for more practice
**Test**
**Chapter 6 Syllabus**
**More on Proofs**
**Section 6.1 define: axiomatic system** - a logical progression from initial statements and definitions to other statements which are based on those initial statements.
assignment: reread Chapter 1
**Section 6.2 Logic and “Indirect” proofs**
review converse
define: inverse and contrapositive
deal with truth tables and logical equivalence (worksheet)
discuss how this leads to the formation of indirect proofs
hw: pp.179-181 all (discuss possible legal uses)
**Sect. 6.3 Review/Classification of theorems-lines @ planes**
define: existence(incidence) - “at least one”
uniqueness - “at most one”
put together: “exactly one” or “one and only one”
review: line and plane postulates (try to name unnamed ones)
then, for each of the line and plane theorems, analyze the __“indirect” proofs__ which are given to prove __uniqueness__.
hw: pp185 - 186 all
**Section 6.4 Perpendiculars**
read pp. 187-191
classify each theorem as an existence or uniqueness theorem
(or both)
analyze proofs of existence and uniqueness
add these to your list to memorize
pp.192-193 #1-14 , 16(bonus)
**Section 6.5 Auxiliary Lines (Sets)**
back up any sets introduced with a postulate/theorem!
read examples carefully and supply a second proof for the first example
hw: pp 198-200 #1-19
**Section 6.6 Added Information for future use**
read pp. 201 - 204
hw: pp205-206 #1-4,6
quiz? prove the “Crossbar theorem” #7
Chapter Test
**Chapter 7 Syllabus**
**Inequalities of one and two triangles**
**Section 7.1** Making reasonable conjectures based on observation
Draw conclusions inductively - give each of the “theorems” a name -that can be remembered! (Don’t use Kovak’s rule, Brian)
hw: pp 212-213 #1-10
**Section 7.2** Inequality properties for numbers (segment lengths, and angles measures)
memorize these!
Paraphrase Thm 2.2:
What is(are) the difference(s) between Thm 2.2 and the Parts theorem?
Add Parts Theorem to your List!
hw: pp215-216 #1-15
:try to prove the exterior angle theorem without looking at the proof provided in the book.
**Section 7.3** The Exterior angle theorem
define: exterior angle, remote interior angle, adjacent interior angle
Add Ext. < Thm. to your list!
hw: pp.219-221 #1-13
**Section 7.4** More Congruence Theorems
Add them to your list!
Read proofs very carefully
hw: pp. 223-224 #1-9
**Section 7.5** Single ∆ ≠ Thms. (What had you named them?)
Add it to your list!
pp. 227 -228 #1-17
**Section 7.6** Distance between a line and a point
Read proofs carefully
make a note of the definition given.
What did you call the ∆ ≠ thm?
hw: pp.231-232 #1-11
**Section 7.7** Two ∆ ≠ theorems
hw: pp. 234-236 all
**Section 7.8**
define altitude: (we’ll talk more about this later)]
Chapter Review and TEST
**Chapter 8**
**Perpendicular Lines and Planes in Space**
writing assignment - Have students outline this chapter, stressing the relationships among the various theorems
__Section 8.1 __define: a line perpendicular to a plane
define: necessary - __prerequisite__ whose falsity assures the falsity of another statement
sufficient - an adjective used to describe a situation where __all of the necessary conditions__ are met to assure the truth of another statement
Objective: to use these terms in describing the Basic Theorem on Perpendiculars
review: Chapter 3 and others
hw: pp.244-245 all
__Section 8.2__ Analyze theorem 8.1
Use triangle congruence to prove that if two points are equidistant from endpoints of a segment then every point betwee those two given points is equidistant from the endpoints of the segment (Used in the Basic Theorem on Perpendiculars)
Review theorem 6.2
If two points are equidistant from the endpoints of a segment, then they determine the perpendicular bisector.
Carefully detail the proof of the Basic Theorem on Perpendiculars.
hw: pp 247-249 all
__Section 8.3__
__ __Theorem 8.3 - Through a given point of a given line there passes a plane perpendicular to the given line.
The proof of almost all of the theorems regarding space depend on their counterparts in a plane. This is true of theorems 8.3 (auxiliary planes drawn) and 6.1 ( the usefulness of having a line perpendicular to a given line in a plane)... The remainder of the proof is basically contingent on the Basic Theorems on Perpendiculars
Theorem 8.4 - If a line and a plane are perpendicular, then the plane contains every line perpendicular the the given line at its point of intersection with the given plane.
Again, this is contingent on the idea that in a plane, there is only one line perpendicular to a given line (Auxiliary plane used)
Theorem 8.5 Uniqueness of the plane perpendicular to the given line
Theorem 8.6 Perpendicular bisecting Plane Theorem - extension of Perpendicular Bisector theorem (prove this!)
hw: pp251-253 #1-14,18,19
__Section 8.4__
Theorem 8.7 - Two lines perpendicular to the same plane are coplanar.
Justify the main steps which are given in the book
Discuss the “method of wishful thinking”.
Theorem 8.8 a composite of theorems 8.3 and 8.5 (However, these only dealt with a given point __on __ the given line)
Theorem 8.9 refer to #18 and 19 of the previous section
(However, these only dealt with a given point __on __ the given line)
The second minimum theorem - The shortest segment to a plane from an external point is the perpendicular segment -- Again, relate this theorem to its two - dimensional counterpart.
define: distance from a point to a plane.
hw: p. 256 all, Chapter Review through #14
Test
**Chapter 9 **
**Parallel Lines in a Plane**
__Section 9.1 Sufficient Conditions for Parallel Lines__
define: parallel, skew
query: What is the difference between the definition of parallel and theorem 9.1?
Analyze proofs carefully - especially the “Parallel Postulate”
hw: pp266-268 #1-10 in class
#11-15
__Section 9.2 More of the Same__
__ __define: corresponding angles, same-side interior angles
hw: pp.271-272 #1-8
__Section 9.3 Formal intro. to the “Parallel Postulate”__
query: How many of these theorems are converses of those theorems found earlier in this chapter?
__ __hw: pp.275-276 #1-11
#12-17, 19 (overheads)
__Section 9.4 Triangle Angle Measures__
Note the relationship between the Parallel Postulate, the sum of the interior angles of a triangle, and hyperbolic geometry.
hw: pp.279-280 #1-15
**Quiz Possible**
__Section 9.5 Intro. to Quadrilaterals__
define: convex, opposite, consecutive, diagonal, parallelogram, trapezoid, base, median
differentiate between the definition of parallelogram and other properties of parallelograms (make note of properties sufficient to prove parallelograms)
Note that there are theorems which deal with the converses of each other.
hw: pp. 285-288 #1-10 individual
#11-27 group work (individual responsibility)
__Section 9.6 Rhombus, Rectangle, and Square__
__ __hw: pp.289-291 #1-10 individual
#11-15 group work (individual responsibility)
**Quiz Possible**
__Section 9.7 Right Triangle Theorems__
Analyze 30° - 60° - 90° triangles
note difference between median of a triangle and median of a trapezoid.
hw: pp. 292-293 #1-12
__Section 9.8 Transversals to many parallel lines__
__ __define: intercept, proportionality
hw: p.296 all
__Section 9.8 Analyze Concurrence Using the Sketchpad__
__ __define: concurrence
Make a note of the special property(ies) of the point of intersection in each case.
medians --
angle bisectors --
perpendicular bisectors --
hw: p.299 #1-5
Review Chapter Set B #1-20
**Chapter Test**
**Honors Geometry- Chapter 10 Syllabus**
**Parallel Lines and Planes**
Note: it will be very helpful to you to analyze this material in light of the information considered in Chapters 8 and 9. For many of the proofs, the introduction
of an auxiliary plane will become essential.
__Section 10.1__
Read pp. 307-311 very carefully, making note of all theorems and any counterparts found in earlier chapters. Analyze proofs carefully!
Theorem 10-1 -
Theorem 10-2 -Note the use of theorems from Chapters 8 and 9 (Review these often!)
Theorem 10-3 - (converse of 10.2?)
Theorem 10-4 - Does this belong in this chapter?
How does the corollary 10-4.1 relate to the theorem?
How does the corollary 10-4.2 relate to the theorem? How is similar to a theorem in the previous chapter? How does it differ?
Theorem 10-5 - Relate this to the previous chapter.
hw: pp.311 - 313 #1-11,13,14
__Section 10.2 Dihedral Angles and Perpendicular Planes__
read pp.313-316 very carefully paying particular attention to the proofs
define: dihedral angle, edge, face, plane angle (Why is a plane angle defined this way?)
Know: how to __measure__ a dihedral angle
define: the interior of a dihedral angle:
hw: pp 317-319 #1-12, Desargues’ Theorem
__Section 10.3 Projections__
define: locus, projection...
hw: p322 #1-10
__Chapter Review - all__
**Polygonal Regions and Their Areas**
**Chapter 11 Syllabus**
__Section 11.1 Area of Polygonal Regions (Part 1) __
__ __define: polygonal region, triangulation
Complete the analogy: Area Postulate: __________ = area: distance
Fill in the blank: Congruent figures have ___________ areas.
State the converse of the above theorem; is this true or false.
State and memorize the Area Addition Postulate.
Areasquare = ________________
Arearectangle = ________________ (pay attention to proof)
hw: pp.334 #1-20
__Section 11.2 Area of Polygonal Regions (Part 2)__
__ __
__derive__ the formula for: Areatriangle = _______________
Construct an acute, right, and obtuse ∆ and label the base and height of each.
__derive__ the formula for: Areaparallelogram = _______________
Areatrapezoid = _______________
Theorem 11.6 is actually an immediate corollary of _______________
What theorem similar to 11.7 could be derived using the same process?
Pay particular attention to the theorems described in #15,18 (memorize these!)
hw: pp. 342-344 #1-18,27
#19-26
__Section 11.3 The Pythagorean Theorem__
__ __Why do you think the authors decided to introduce this theorem at this point in the book?
Locate and copy one other proof of the Pythagorean theorem other than the one(s) given in the book.
State the two cases which would represent the contrapositive of the Pythagorean theorem. How do you know these are true? Where might these theorems be utilized:
Case 1:
Case 2:
hw: pp347 - 350 #1-27 odd (memorize your chart for #7b)
#2-26 even
__Section 11.4 “Special” Right Triangles__
Derive the length of the hypotenuse of an isosceles right triangle.
Derive the length of the longer leg of a 30° - 60° - 90° triangle.
hw : pp. 353 - 355 #1-28
Chapter Review
**Similarity and Proportions**
**Chapter 12 Syllabus**
Section 12.1
define: similarity (informally), proportion -- note likeness to analogies
, geometric mean
review: correspondence
Objective 1) recognize notation used in stating proportionality / similarity
~ symbol has two related meanings
2) Theorem 12.1 Proportionality is an equivalence relation
3) recognize patterns -> properties of proportions
hw: pp365-367 #1-19
Section 12.2
define: similarity (formally) -- CASTCSP
hw: pp 370-372 #1-19
Section 12.3
Objective 1) familiarize yourself with the “Basic Proportionality Theorem” --
complete the details of the proof and Memorize!
Also, state all of the proportions which could be easily derived from the result of this theorem:
2) familiarize yourself with the converse also.
analyze the proof and memorize
Find one other theorem which had a similar method given in the proof (from the book in an earlier chapter)
hw: pp 375 - 379 #1-20
Section 12.4 “Shortcuts to proving similar triangles”
AA Similarity Theorem:
“Triangle Chop” Corollary:
hw: pp382 - 384 #1-21
Prove: Similarity is an equivalence relation
Similarity Substitution Corollary
Memorize and Analyze the Proofs of the SAS and SSS Similarity Theorems
hw: pp388 - 390 #1-11 and Honors problem
Section 12.5 Geometric Mean Theorems
Memorize these (be sure you know what the words are saying)
hw: pp 392 - 394 #1-10
Section 12.6 Ratio of Areas/ Volumes
if scale factor of two similar figures is a:b, then ratio of areas is a2 : b2
, then ratio of volumes is a3: b3
hw: pp396 -398 #1-17, 21,22,24
Review for Test
Test
**Coordinate Geometry - Ch 13 Syllabus**
Read entire Chapter
__Section 1 and 2__
define: ordered pair, x and y coordinate, Cartesian plane
do pp.406-407 #4, 10, 16
__Section 3__
__ __do pp. 411-412 #8, 9, 12
__Section 4__
__ __define: slope
do pp. 417 -418 #6,9,12
__Section 5__
__ __properties of parallel and perpendicular lines
do pp. 422 -423 #6, 9, 16
__Section 6__
__ __define: write a formula for... the distance between two points,
the distance from a point to a line
__ __do pp. 425 #10, 18
__Section 7__
__ __write a formula for midpoint as a function of the endpoints
do p. 430 #6,10
__Section 8__
__ __properties of the midpoint of the hypotenuse of a right triangle
do p.435 #2, 3
__Section 9__
__ __graphing inequality conditions
do pp. 438-439 #6,9,13
__Section 10__
__ __forms for linear equations
do pp. 444 #4, 10, 12
**Chapter 14 Syllabus**
**Circles and Spheres**
Many of the theorems in this Chapter are founded upon congruent or similar triangles.
Therefore, you should become familiar with most of them.
__Section 14.1__
define: locus, circle, sphere, center, radius, concentric, diameter, secant, chord,
great circle
Objective: to construct a circle given: a) the center and radius
b) the center and a point on the circle
pp. 452-453 # 1-11
__Section 14.2__
define: tangent, interior, exterior, point of tangency, internally tangent, externally tangent, equidistant
Objectives: 1) to create a diagram which will remind you of the necessary theorem
from the section
2) construct a circle given any three points that lie on the circle
pp.455-457 #1-18
pp. 460-462 #1-13
__Section 14.3__
This section corresponds to Section 14.1 and 14.2, incorporating the 3rd dimension.
pp. 465 - 466 #1-10
__Section 14.4__
define: central angle, minor arc, major arc, semicircle, degree measure
Objectives: 1) To determine the measure of an arc, given the necessary information
2) To determine the measure of an angle, given the necessary arc info.
pp.469-470 #1-9
__Section 14.5__
define: inscribed angle, intercepted arcs, inscribed polygon, circumscribed polygon
Objectives: 1) To determine the measure of an arc, given the necessary information
2) To determine the measure of an angle, given the necessary arc info.
(similar to section 14.4)
pp.474-476 #1-19
__Section 14.6__
define: congruent arcs, congruent circles
Objectives: 1) To determine the measure of an arc, given the necessary information
2) To determine the measure of an angle, given the necessary arc info.
(similar to section 14.4)
pp. 478-480 #1-18, 19-28
__Section 14.7__
define: secant segment, the “power” of a circle and a point
Objective: 1) to determine the length of a given chord or segment, based on given info.
pp.485-488 #1-29
__Section 14.8__
Objectives: 1) to determine the equation of a circle, given the center and radius
2) to determine the equation of a circle, given the center and a point of
the circle.
3) to graph a circle, given its equation
pp. 492-495 #1-33
**Chapter 15 Syllabus**
**Characterizations or Loci**
__Section 15.1 and 15.2__
definition: a “characterization” or “locus” is the set of __all points __ which satisfy given characteristics or requirements.
We have dealt with some of these in previous chapters. For each of the following, specify what characteristics determine the following loci:
perpendicular bisector
angle bisector
circle
sphere
interior of a circle
note --To test if your description is specific enough: If you would read your description to someone else, would they be able to conceptualize (or draw) what you have stated?
-- also try not to restate the conditions in the name of the locus
note -- If the conjunction “and” is used in the description, consider thinking of the locus as the intersection of two simpler loci.
hw: pp. 503-505 #1-27 excluding #22
and pp. 506 #1-9 (to be done over a period of two days)
__Sections 15.3 - 15.5__
define: concurrent
Complete the following chart:
__intersecting lines name of point characteristics of point__
Perpendicular bisectors of ∆
Altitudes of ∆
Medians of ∆
Angle bisectors of ∆
Distribute “sketchpad” overview
Lab work (two days)
p. 509 - 510 #1-8
p. 512 - 513 #1-8
p. 515 - 516 #1-5
p. 527 #1-10
Test on Chapter 15
**Areas of Circles and Sectors**
**Chapter 16 Syllabus**
__Section 16.1__
define: polygon
objectives: 1) to use all prefixes denoting polygons correctly
2) to differentiate between a concave and convex polygon
3) to determine the number of diagonals in a convex “n-gon”
4) to determine the sum of the measures of the interior and exterior angles
in a convex “n-gon”
Arrive at formulas “discreetly”
pp. 537-539 #1-17
__Section 16.2__
define: regular polygon, apothem
objectives:1) to determine the measure of each interior (or exterior) angle of a regular
polygon
2) to determine the area...
pp.540 - 541 all
__Section 16.3__
__C__ = π discuss the “method of exhaustion”
d discuss “limits”
pp.544-545 #1-14
__Section 16.4__’
define: annulus
Continue discussion of “ the method of exhaustion and limits”
pp. 547-549 #1-21
__Section 16.5 __
define: arclength (as opposed to arc measure), sector
Continue discussion of “ the method of exhaustion and limits”
pp.552-553 #1-18 all
**Ch. 16 Test**
**Solid Geometry**
**Chapter 19 Syllabus**
note: unlike a sphere, these figures are __solid __(include interior points)
__Section 19.1__
define: prism (right and oblique), altitude, base, lateral face, cross - section, lateral
edge, base edge, parallelepiped, rectangular parallelepiped, cube, lateral area,
base area
objective: 1) to determine lateral area of a prism or parallelepiped
2) to determine various cross - sectional areas
pp. 629-630 #1-14 excluding #9
__Section 19.2__
define: pyramid, vertex, altitude, ... slant height
objective: 1) to determine lateral area of a right pyramid
2) to determine various cross - sectional areas
pp. 634 - 636 all
__Section 19.3__
Discuss Cavalieri’s principle, limits, and the method of exhaustion (in determining volumes)
Note the differences among the given proofs.
read this section carefully
pp. 641-643 #1-16
worksheet on Cavalieri’s principle
__Section 19.4__ __ and 19.5 __
Discuss relationship between sections 19.3 and 19.4
pp.647-649 all , 652-653 #1-12,16-18
**Chapter 19 Test** |