Geometry

Practice n1,2,3,4,5,6,7 p.310 __Chapter 3.3 Constructing Perpendiculars to a Line p.152-__ Chapter 3.3 __Classwork.__ Conjecture C-7 p.153 (enter //perpendicular segment// in the blank space). Definition of altitude and altitudes in different triangles p.154. Practice. #1-5 p.154. For class notes click on the link above. __Homework assigned on 10.28 for 10.29.2009 problems__ __Chapter 3.4 Constructing Angle Bisectors p.157__ Conjecture C-8 p.157 (enter equidistant) in the blank space. Practice Your Skills Lesson 3.4 #2-4. __Chapter 3.5 (Constructing Parallel Lines) Slopes of Parallel and Perpendicular Lines (p.165-)__ Parallel and Perpendicular Slope Properties (p.165). Study examples A and B on p.166. Practice: p.167 #1-4, 7. Classroom theory notes link. Classroom practice notes link. __Homework assigned on 10.30 for 11.02.2009__ p.167 #8-10. Hints: In #8 and #9 use slope=rise/run. Lines tilted to the left have a negative slope, lines tilted to the right have a positive slope. Compare the slopes, keeping in mind properties #1 and #2 on page 165. Then, recall properties of special quadrilaterals: trapezoid (p.62), parallelogram, or rectangle (p.63). If all slopes are different and none is a opposite reciprocal of at least one of them, you have an ordinary quadrilateral. In # 10a find slopes for the lines HA, AN, VD, and DH using the slope formula on page 133. Then use the considerations above. In 10b use the midpoint formula on page 36. Chapter 3.5 (Constructing Parallel Lines) Slopes of Parallel and Perpendicular Lines. Day 2 (p.165-)
 * 1) 11 p.167. Determine slopes of the quadrilateral sides by using slope formula and by using the ratio rise/run after plotting the vertices on the grid paper.

November 04, 2009. CONSTRUCTED RESPONSE 5 Constructed Response 5. Possible Solution.

__November 05, 2009 Chapter 4.1 Triangle Sum Conjecture p. 198__ Click here for Ch.4.1 Classroom Notes Classwork. Read Investigation The Triangle Sum on p. 199 (we did it once in class).Triangle Sum Conjecture C-17 p.199 (add 180 degrees in the blank space with?); Third Angle Conjecture C-18 p.200 (add is equal in measure to the third angle in the other triangle in the blank space with ?). Read example with solution on p.201. Practice. #2, 4, 6,7 p.201. For Conjectures' demonstrations click on the links below. Triangle Sum Conjecture Demonstration Third Angle Conjecture Demonstration __Homework assigned on 11.05 for 11.06.2009__ p.201 #5, p.202 #8

__November 06, 2009 Chapter 4.2 Properties of Special Triangles p.204__ Click here for Ch.4.2 Classroom Notes Definitions: vertex angle, base angles, base, legs (p.204). Know the spelling of __//**isosceles.**//__ //Isosceles Triangle Conjecture// (C-19) on page 205: If a triangle is isosceles, //then its base angles are congruent//. //Converse of the Isosceles Triangle Conjecture// (C-20) on page 206: If a triangle has two congruent angles, //then it is an isosceles triangle.// // Practice: p.206 #1-3. For each problem make a sketch, write what is given and what you have to determine. Show calculations and explain (refer to corresponding conjectures) // // __Homework assigned on 11.06 for 11.09.2009__ //

__November 09, 2009 Substitute__ __November 10, 2009 Chapter 4.2 Writing LInear Equations p.210-__ __Click here for Classroom Notes__ Read examples A, B, and C on p.211. Practice: p.212 #1, 3, 4, 5, 6.

__November 12, 2009 Chapter 4.2 Writing Linear Equations. Determine Slopes of the Lines.__ __Click here for November 12 Classroom Notes__ Alg 1 Practice Workbook Ch.5.2

__November 13, 2009 Chapter 4.2 Writing Linear Equations. Determine Slopes of the Lines. Day 2(3).__ __Click here for November 13 Classroom Notes __ Alg 1 Practice Workbook Ch.5.4

November 16, 2009 Chapter 4.3 Triangle Inequalities p.213- Read Investigations 1-3 and fill in the the blank spaces with question marks: C-21 write //__greater than__//; C-22 write __//larger than the angle opposite the shorter side//__; C--23 write __//is equal to the sum of the measures of the remote interior angles.//__ Know the definitions of //exterior angles, adjacent interior//, and //remote interior angles.// Practice: p.216-217 #1-4, 7, 8, and 15. Conjecture C-21 Investigation Conjecture C-22 Investigation Conjecture C-23 Investigation __Homework assigned on 11.16 for 11.17.2009__ p.216-217 # 6, 9, 16

November 17, 2009 Chapter 4.4 Congruence Shortcuts p.219- Know the definitions of __//included angle//__ and __//included side//__ p.219. For C-24 SSS Congruent Conjecture in the blank space with a question mark write __//the triangles are congruent//__. For C-25 SAS Congruence Conjecture in the blank space with a question mark write //__the triangles are congruen__t.// Classwork #1-6 p.222. __Homework assigned on 11.17 for 11.18.2009:__ #20 p.224.

__November 18, 2009 Number 6 Constructed Response__ The Constructed Response Answe__r__

November 19, 2009 Chapter 4.5 Are There Other Congruence Shortcuts p.225- For C-26 ASA Congruence Conjecture p.225 and in C-27 SAA Conguence Conjecture in blank spaces with question marks write the //__triangles are congruent.__// Work on problems #1-6 p.227, #13 and 15 p.228 __Homework assigned on 11.19 for 11.20.2009__ p.228 problem 10 p.228 problem 11 p.228 problem 12

__November 20, 2009 First Benchmark results__

__November 23 and 24, 2009 Chapter 4.6 Corresponding Parts of Congruent Triangles p. 230__ Definition of CPCTC p.230 (top). Read examples A and B on p.230. Practice: p.231 #1-2.

__November 25, 2009 Geom Constructed Response 7__ __Possible Answer to the Constructed Response 7__

November 30, 2009 Chapter 4.8 Proving Isosceles Triangle Conjectures p.242 Vertex Angle Conjecture C-28, p.242 //In an isosceles triangle, the bisector of the vertex angle ia also the altitude and the median to the base.// Equilateral/Equiangular Triangle Conjecture C-29, p.243 //Every angle triangle is equiangular, and, conversely, every equiangular triangle is equilateral.// Geom Sketch 5 C-28 Investigation __Geom Sketch 5 C-29 Investigation__ Practice: p.243 #1-3, p.245 #11 __Homework assigned on 11.30 for 12.01.2009 Ch.4.8 Computer Generated__ __Solutions to the homework problems__

__December 01, 2009 Chapter 4 Review__

__December 02, 2009 Chapter 4 Review Geometry Constructed Response 8__ Copy of constructed response 8

__December 04, 2009 Chapter 4 Discovering and Proving Triangle Properties Test__

December 07, 2009 Chapter 5.1 Polygon Sum Conjecture p.256 Recall some facts about polygons on p.54. Conjectures: C-30 (p.256) blank space - //360 degrees//; C-31 (p.256) blank space - //540 degrees//; C-32 (p.257) blank space - //180(n-2).// Practice: p.257 # 31, 4, 5 __Homework assigned on 12.07 for 12.08.2009 p.257 2, 3; p.258 6, 7__ p.257 number 3 p.258 number 6 Number 2 p.257

December 08, 2009 Chapter 5.2 Exterior Angles of a Polygon p.260 Definition of an //exterior angle// p.260. For Conjecture C-33 p.261 enter //360 degrees// in blank space. For Conjecture C-34 Equiangular Polygon Conjecture p.261 enter //189-360/n//, //(180(n-2))/n// in blank space. Practice: p.262 #4, 5, and 6 (optional) Homework assigned on 12.08 for 12.09.2009 p.262 7.

__December 09, 2009 9th Constructed Response__

__December 10, 2009 Chapter 5.3 Kite Properties p.266__ Start exploring properties of a kite using Cabri Geometry Jr on graphing calculators. __//Kite//__ is a quadrilateral with exactly two distinct pairs of congruent consecutive angles. The two angles between each pair of congruent sides of a kite are called vertex angles, the other pair are called nonvertex angles 9p.266) //C-35 The nonvertex angles of a kite are congruent.// //C-36 The diagonals of a kite are perpendicular.// //C-37 The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.// //C-38 The vertex angles of a kite are bisected by a diagonal.// Practice: p.269 #1,2. __Homework assigned on 12.10. for 12.11.2009 p.270 n5.__

December 11, 2009 Chapter 5.3 Kite and Trapezoid Properties p.266

__December 14, 2009 Investigate Properties of Kites using Cabri Jr Geometry__ __Chapter 5.4 Properties Of Midsegments p.273__ C-42 (p.273) The three midsegments of a triangle divide it into //four congruent triangles.// C-43 (p.274) A midsegment of a triangle is //parallel// to the third side and //half// the length of //the third side.// C-44 (p.275) The midsegment of a trapezoid is //parallel// to the bases and is equal in length to the //average of the lengths of the bases.//

__December 15, 2009 Investigate Properties of Isosceles Trapezoid using Cabri Jr Geometry on Graphing Calculators.__ Describe the Investigations. Preclass Quiz on Properties of Kite __Homework Assigned on 12.15 for 12.16. 2009 p.275 n.3 p.276 n.5 and 6__

__December 17-18, 2009. 2nd Geometry Benchmark.__

__December 22, 2009 Chapter 5.5 Properties of Parallelograms p.279-__ __**Parallelogram**__ - quadrilateral in which opposite sides are parallel. Review concepts and vocabulary. The Parallelogram Cabri Jr Investigations on graphing calculators After the investigations the conjectures should read the following: C-45 The opposite angles of a parallelogram are //congruent// C-46 The consecutive angles of a parallelogram are //supplementary.// C-47 The opposite sides of a parallelogram are //congruent.// C-48 The diagonals of a parallelogram //bisect each other//

__December 23, 2009 Chapter 5.5 Part 2 Properties of Parallelograms. Practice__

January 04, 2010 Discuss Benchmark 2 (see December 17-18 above)

__January 05, 2010 Chapter 5.6 Properties of Special Parallelograms p.287__ __**Rhombus**__ is a parallelogram in which all sides are congruent. RHOMBUS DIAGONALS CONJECTURE **C-50** (p.288). The diagonals of a rhombus are //perpendicular// and they //bisect// each other. RHOMBUS ANGLES CONJECTURE **C-51** (p.288). The //diagonals// of a rhombus //bisect// the angles of the rhombus. RECTANGLE DIAGONALS CONJECTURE **C-52** (p.289) The diagonals of a rectangle are //congruent// and //bisect each other.// SQUARE DIAGONALS CONJECTURE **C-53** (p.290) The diagonals of a square are //congruent, perpendicular,// and //bisect each other.// Practice p.291 #14-16. Homework assigned on 01.05 for 01.06.2010 p.290 numbers 11, 12, 13
 * Parallelogram** is a quadrilateral in which opposite sides are parallel (have equal slope)
 * __Rectangle__** - equilateral parallelogram.
 * __Square__** - equiangular rhombus or **__Square__** - equilateral rectangle.

__Chapter 5 Discovering and Proving Polygon Properties Test Review Questions (Answers below in parts 1 and 2)__ __January 06, 2010 Chapter 5 Test Review Part 1 Answers__ January 07, 2010 Chapter 5 Test Review Part 2 Answers __January 08, 2010 Chapter 5 Test. See Review with Solutions Above__

__January 11, 2010 Chapter 6.1 Chord Properties p.306__ Copy definitions of: //circle, radius, diameter// (p.67); //congruent circles, concentric circles, arc of a circle, endpoints of the arc, semicircle, minor arc, major arc, arc measure, central angle// (p.68); Answers to the activity on top of the page 306: 1F, 2E, 3C, 4A, 5D, 6B, 7G, 8I, 9H. //A central angle has its vertex at the center of the circle (Investigation 1 p.307)// //An inscribed angle has its vertex on the circle and its sides are chords (Investigation 1 p.307)// Read and understand conjectures on p.308-310. C-54 (p.308) //congruent;// C-55 (p.308) //intercepted arcs;// C-56 (p.309) //bisector;// C-57 (p.309) //equidistant;// C-58 (p.310) //passes through the center of the circle.// __Discovery practice using Cabri Cabri Jr Geometry on graphing calculators.__

__January 12, 2010 Chapter 6.1 Chord Properties Part 2.__ __Practice n1,2,3,4,5,6,7 p.310__ __Homework assigned on 01.12 for 01.13.2010 p.317 number 20.__

__January 13, 2010 Chapter 6.2 Tangent Properties p.313__ __Conduct investigation on graphing calculator using Cabri Jr Geometry for C-59 and C-60.__ //Tangent// ia a line that intersects the circle only once. //Chord// is a line segment whose endpoints lie on the circle. //Diameter// is a chord that passes through the center of the circle. A diameter is the longest chord. __Conduct investigations on graphing calculators using Cabri Jr geometry.__ C-59 (p.313) A tangent to a circle //is perpendicular to// the radius drawn to the point of tangency. C-60 (p.314) Tangent segments to a circle from a point outside the circle are //congruent.// Explore the definition of //tangent segments// on p.314 //Tangent circles// are two circles that are tangent to the same line at the same point. They can be //internally tangent// or //externally tangent// (explore these definitions on top of page 315) __Homework assigned on 01.13 for 01.14.2010 p.315 number 3.__ __Homework part 2 p.315 numbers 4 and 5.__

__January 14, 2010 Chapter 6.3 Arcs and Angles p.319__ An //arc of a circle// - two points on the circle and the continuous (unbroken) part of the circle between the two points. A //semicircle// - arc of a circle whose endpoints are the endpoints of the diameter. A //minor arc// is an arc of a circle that is smaller than a semicircle. A //major arc// is an arc of a circle that is larger than a semicircle. You find the arc measure by measuring the central angle. A //central angle// has its vertex at the center of the circle, and sides passing through the endpoints of the arc (p.68) An //inscribed angle// has its vertex on the circle and its sides are chords. C-61 p.319 The measure of an angle inscribed in a circle //is one-half the measure of the central angle.// C-62 p.320 Inscribed angles that intercept the same //are congruent.// C-63 p.320 Angles inscribed in a semicircle //are right angles.// Homework assigned on 01.14 for 01.15.2010 numbers 5 and 6 __p.322__

__January 15, 2010 Chapter 6.3 Arcs and Angles Part 2.p.321__ A quadrilateral inscribed in a circle is called a //cyclic// quadrilateral. C-64 p.321 The //opposite// angles of a cyclic quadrilateral are //supplementary// (the sum is equal to 180 degrees). C-64 Investigation was conducted on graphing calculators using Cabri Jr Geometry. C-65 p.321 Parallel lines intercept //congruent// arcs on a circle.

__January 19, 2010 Chapter 6.5 The Circumference/Diameter Ratio p.331__ The distance around a polygon is called the perimeter. The distance around the circle is called the //circumference (p.331)// The investigation of the conjectures is conducted on graphing calculatores using Cabri Jr Geometry. C-66 p.332 If C is the circumference and d is a diameter of a circle, then there is a number such as ¶ (3.14) such that C = ¶//d//. If d = 2r where r is the radius, then C = 2¶//r.// Practice: #1-6 p.333. __Homework assigned on 01.19 for 01.20.2010 numbers 7,8,9,10 p.334__

__January 20, 2010 Chapter 6.7 Arc Length p.341__ The //length of an arc//, or arc length, is some fraction of the circumference of its circle. C-67 The length of an arc equals the circumference times the measure of the central angle divided by 360 degrees. Practice p.343 # 1-3. __Homework assigned on 01.20 for 01.20.2010 numbers 4 and 5 on p.343__

January 21, 2010 Chapter 6 Review

__January 22, 2010 Chapter 6 Test__

__January 25-26, 2010 Chapter 8.1 Areas of Rectangles and Parallelograms p.410__ The //area// of a plane figure is the measure of the region enclosed by the figure. Any side of rectangles can be called a //base//. A rectangles's //height// is the length of the side that is perpendicular to the base. __C-75__ p.411 The area of a rectangle is given by the formula //A=bh//, where //A// is the area, //b// is the length of the base, and //h// is the height of the rectangle. //An altitude// is any segment from one side of a parallelogram perpendicular to a line through the opposite side. The length of the altitude is the height. __C-76__ p.412 The area of a parallelogram is given by the formula A=bh, where A is the area, b is the length of the base, and h is the height of the paralleogram.

__January 27, 2010 Chapter 8.2 Areas of Triangles, Trapezoids, and Kites p.417__ C-77 p.417 The area of a triangle is given by the formula A=0.5bh, where A is the area, b is the length of the base, and h is the height of the triangle. C-78 p.418 The area of a trapezoid is given by the formula A=0.5(b1+b2)h, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid. C-79 p.418 The area of the kite is given by the formula A=0.5d1d2, where d1 and d2 are the lengths of the diagonals. __Homework assigned on 01.27 for 01.28.2010 p.419 n.8, 10, 12 (extra credit)__

__January 28, 2010 Chapter 8.4 Areas of Regular Polygons p.426__ Definition of //apothem// p. 426 __C-80__ p.427 The area of a regular polygon is given by the formula //__A=0.5asn__//, where //A// is the area, //a// is the apothem, //s// is the length of each side, and //n// is the number of sides. The length of each side times the number oof sides is the perimeter, //P//, so //sn=P//. Thus you can write the formula for the area as __//A=0.5aP//__ __Homework assigned on 01.28 for 01.29.2010 p.427 n.5, 7, 8__

__January 29, 2010 Chapter 8.5 Area of Circles p.433__ __Homework assigned on 01.29 for 02.01. 2010__

__February 02 and 03, 2010 Chapter 8.6__ Definition of a sector of a circle, segment of a circle, and annulus on p.437. Examine the formulas and the drawings on the bottom of the page 437. Study examples on p.438. Practice p.439 n.1, 4, 6. __Homework assigned on 02.02 for 02.03.2010 p.439 n. 3, 5, 8__

__February 03, 2010 Chapter 8.7 Surface Area__ Definition of: surfac//e area, bases, and lateral faces// p.445; //slant height// p.447. __Homework assigned on 02.02. for 02.04.2010 p.450 n.2, 5, 6.__

__February 04, 2010 Chapter 8 Review Practice__ p.455 #1-10, p.456 #19, 26, p.457 #29 __Homework assigned on 02.04 for 02.05.2010 p.450 n.9__

__February 19, 2010 Chapter 9.1 The Theorem of Pythagoras p.462__ __Homework assigned on 02.19 for 02.22.2010 p.465 n.9 and 11__

__February 22, 2010 Chapter 9.2 The Converse of the Pythagorean Theorem p.468__ Practice: p.470 #1-6; p.474 #1-4. __Homework assigned on 02.22 for 02.23.2010 p.470 n.7 and 8 p.474 n.12 and 14.__

__February 23, 2010 Chapter 9.3 Two Special Right Triangles p.475__ Practice: p.477 #1-5 Homework assigned on 02.23 for 02.23.2010 p.477 n.6 p.478 n.8

__March 01, 2010 Chapter 9.5 Distance in Coordinate Geometry p.486-__ Distance formula C-86 p.487, equation of a circle C-87 p.488 Practice p.489 n1-3. __Homework assigned on 03.01 for 03.02.2010 p.489 n.5__

__March 04 Chapter 9 Pythagorean Theorem Review__

__March 05, 2010 Chapter 9 Test__

__March 08, 2010 Chapter 10.1 The Geometry of Solids p.504__ Definitions (p.505-508): //polyhedron, regular polyhedron, face, lateral face, edge, lateral edge, vetex, prism, right prism, oblique prism, base, height, altitude, tetrahedron, pyramid, sphere, hemisphere, great circle, cylinder, axis, right cylinder, oblique cylinder, cone, right cone, oblique cone.//

__March 09, 2010 Chapter 10.2 Volume of Prisms and Cylinders p.514__ __Homework assigned on 03.09 for 03.10.2010 p.518 n.7d, 7g, 7j.__

__March 11, 2010 Chapter 10.3 Volume of Pyramids and Cones p.522-__ Solve problems #1-3 p.524, #(10a, d, g, j) p.525. __Homework assigned on 03.11 for 03.12.2010 p.524 n.4 and 6.__

__March 12, 2010 Ch 10.3 Practice p.525 n.10b, 10e, 10h, 10k.__

March 15, 2010 Chapter 10.4 p.532 n.7, 8 p.533 n.11

March 16, 2010 Chapter 10.5 Displacementand Density Notes p.535-

__March 17, 2010 Benchmark 3 Review Notes__

__March 22, 2010 Chapter 10.6 Volume of a Sphere p.542-__ Solve problems 4-6 p.543 __Homework assigned on 03.22 for 03.23.2010 p.555 n11,12__

__March 23, 2010 Chapter 10.7 Surface Area of a Sphere p.546-__ Solve problems 5,6,10a p.548 __Homework assigned on 03.23. for 03.24.2010 p.547 n.2,3 p.548 n.4__

__March 24, 2010 Chapter 10 Volume Review__

__March 30, 2010 Notes__

__April 05, 2010 Notes__

__April 08, 2010 Notes__

__April 09, 2010 Notes Chapter 11.3 Indirect Measurement with Similar Triangles p.581__ Practice: n.1-3 p.582, n.5,7 p.583 __Homework assigned on 04.09 for 04.12.2010 n.7 p.614, n.17 p.616__

__April 12, 2010 Notes Chapter 11.4 Corresponding Parts of Similar Triangles p.586-__ C-96: If two triangles are similar, then the corresponding //altitudes; medians; angle bisectors// are //proportional// to to the corresponding sides. Practice: p.588 n.1-2; p.589 n4,5

__April 13, 2010 Notes Chapter 11.4 Part 2__ p. 588 C-97: A bisector of an angle in a triangle divides the opposite side into segments whose lengths are in the same ratio as //the lengths of the two sides forming the angle.// Practice: n.6-9 p.589

__April 14, 2010 Notes Chapter 11.5 Proportions with Area and Volume__ C-98 p.593. Practice p.595 n.1-3 Homework assigned on 04.14 for 04.15.2010 n.4,5 p.595

__April 15, 2010 Notes Chapter 11.5 Part 2__

__April 16, 2010 Discuss Benchmark 3__

April 19-20, 2010. Notes Chapter 11.6 Proportional Segments Between Parallel Lines (p.603-) Homework assigned on 04.20 for 04.21.2010 p.608 n8,10

__April 21, 2010 Notes Chapter 11.6 Part 2 Practice__ __Homework assigned on 04.20 for 04.21.2010 p.608 n.12__

April 22-23, 2010 Chapter 11 Review

__April 26-27, 2010 Chapter 11 Similarity Test__

__April 28, 2010 Chapter 12.1 Trigonometric Ratios p.620-__ Key concepts (words) opposite/adjacent sides, ratio, sine, cosine, tangent.

April 29, 2010 Practice Trigonometric Ratios Notes Homework assigned on 04.29 for 04.30.2010 p.625 n.9, 18, 19

__April 30, 2010 Practice 2 Trigonometric Ratios Notes__ __Homework assigned on 04.30 for 05.03.2010 n.25, 27 Practice workbook ch12.1__

May 03, 2010 Chapter 12.2 Problem Solving with Right Triangles Notes p.627 __Homework assigned on 05.03 for 05.04.2010 p.62-629 n.2,8__

May 04, 2010 Chapter 12.3 The Law of Sines Notes __Homework assigned on 05.04 for 05.05.2010 p.637 n7,8__

__May 05, 2010 Constructed Response__

__May 06, 2010 Chapter 12 Trigonometry Review__

June 01, 2010 Geometry Final Review Part 1 Q1-11 June 02, 2010 Geometry Final Review Part 2 June 03, 2010 geometry Final Review Part 3 __June 04, 2010 Geometry Final Review Part 4__ __June 07, 2010 Geometry Final Review Part 5__