Geometry Chapter 8 & 11 Capacity Matrix Quadrilaterals and Areas of Polygons and Circles Learning Targets: The student can: 1. Learn all the quadrilaterals and their attributes. (All of Ch 8) 2. Solve geometric problems using the quadrilateral properties. (All of Ch 8) 3. Interpret units of measurement in formulas, including units used in dimensional analysis. (All of Ch 11) 4. Explain proofs or reasoning related to theorems about parallelograms. Theorems include, but are not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. (All of Ch 8) 5. Explain proofs or reasoning related to theorems about circles. Include proof that all circles are similar. (Ch 11) Section Required Assignments Additional Resources Sec 8-1 Angles of Polygons (Formative Assessments) Sec 8-2 Parallelograms (Formative Assessments) Sec 8-3 Tests for Parallelograms (Formative Assessments) Sec 8-4 Rectangles (Formative Assessments) Sec 8-5 Rhombi and Squares (Formative Assessments) Sec 8-6 Trapezoids (Formative Assessments) Chapter 8 Project Chapter 8 Triple Entry Journal Sec 8-1 # s 1-12 Sec 8-1 # s 13, 15, 21, 23, 27, 29, 31 (7 questions) Pg 769 Lesson 8-1 # s 1-12 N2 Properties of parallelograms (ixl) Sec 8-2 # s 17, 19, 21-31 (13 questions) Sec 8-2 # s 1-15 Pg 769 Lesson 8-2 # s 1-16 N3 Proving a quadrilateral is a parallelogram (ixl) N4 Properties of rhombuses (ixl) N5 Properties of squares and rectangles (ixl) N7 Properties of kites (ixl) N1 Classify quadrilaterals (ixl) N6 Properties of trapezoids (ixl) N8 Review: properties of quadrilaterals (ixl) Chapter 8 Project Sec 8-3 # s 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 (10 questions) Sec 8-3 # s 1-12 Pg 769 Lesson 8-3 # s 1-10 Sec 8-4 # s 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33 (11 questions) Sec 8-4 # s 1-9 Pg 770 Lesson 8-4 # s 1-18 Sec 8-5 # s 13, 15, 17, 19, 21, 23 (6 questions) Sec 8-5 # s 1-11 Pg 770 Lesson 8-5 # s 1-8 Sec 8-6 # s 9, 11, 13, 15, 17, 23, 25, 26-28 (10 questions) Sec 8-6 # s 1-8 Pg 770 Lesson 8-6 # s 1-8
Sec 11-1 Areas of Parallelograms (Formative Assessments) Sec 11-2 Areas of Triangles, Trapezoids and Rhombi (Formative Assessments) Sec 11-3 Areas of Regular Polygons and Circles (Formative Assessments) Sec 10-1 Circles and Circumferences (Formative Assessments) Sec 10-2 Angles and Arcs (Formative Assessments) Quiz on Sec 11-1 to 11-3, 10-1 & 10-2 Summative Assessment Must score > 70 Sec 11-4 Areas of Irregular Figures (Formative Assessments) Sec 11-5 Geometric Probability (Formative Assessments) Sec 11-1 # s 9, 11, 13, 15, 17, 21, 23, 25, 27 (9 questions) S1 Perimeter (ixl) S2 Area of rectangles and squares (ixl) Sec 11-2 # s 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35 (12 questions) S3 Area of parallelograms and triangles (ixl) S4 Area of trapezoids (ixl) Sec 11-3 # s 9, 11, 13, 15, 17, 19, 27, 29 (8 questions) Sec 10-1 # s 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 45, 47, 53, 55 (17 questions) S7 Area and circumference of circles (ixl) Sec 10-2 # s 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37 (12 questions) Things you should know: How to compute the area of a parallelogram, triangle, trapezoid, rhombi, regular polygons, circles? Can you find the area of shaded regions by finding the 2 areas and either adding/subtracting them? What is the slope formula? What is the distance formula? How do you find the circumference of a circle? How do you find the area of a sector? How do you find the arc length of a circle? Sec 11-4 # s 9, 11, 13, 15, 17, 19, 21 (7 questions) S6 Area and perimeter in the coordinate plane II (ixl) S8 Area of compound figures (ixl) S9 Area between two shapes (ixl) Sec 11-5 # s 7, 9, 11, 13, 15, 17, 19, 21, 23 (9 questions) Sec 11-1 # s 1-8 Pg 776 Lesson 11-1 # s 1-7 Sec 11-2 # s 1-12 Pg 776 Lesson 11-2 # s 1-11 Sec 11-3 # s 1-7 Pg 777 Lesson 11-3 # s 1-7 Sec 10-1 # s 1-15 Pg 773 Lesson 10-1 # s 1-10 Sec 10-2 # s 1-13 Pg 774 Lesson 10-2 # s 1-12 Sec 11-4 # s 1-7 Pg 777 Lesson 11-4 # s 1-6 Sec 11-5 # s 1-6 Pg 777 Lesson 11-5 # s 1-6
Quiz on Sec 11-4 & 11-5 Summative Assessment Must score > 70 Things you should know: Take home quiz on geometric probability. Topics include SohCahToa, Special Right Triangles, Geometric Means, Pythagorean Theorem, Law of Sines & Law of Cosines. Chapter 8 & 11 Review Chapter 8 Study Guide & Review pg 452 # s 1-34 Chapter 10 Study Guide & Review pg 581 # s 1-28 Chapter 11 Study Guide & Review pg 628 # s 1-20 Chapter 11 Project Chapter 8 & 11 Test Chapter 11 Project (Summative Assessment: Must score > 70.) Chapter 8 & 11 TEST (Summative Assessment: Must score > 70.) Ch 8 Practice Test pg 457 # s 1-15, 18, 19 Ch 11 Practice Test pg 631 # s 1-20
Chapter 8 & 11 Triple Entry Journal Word Definitions Picture and/or Example diagonal (pg 404) isosceles trapezoid (pg 439) kite (pg 438) parallelogram (pg 411) rectangle (pg 424) rhombus (pg 431) square (pg 432) trapezoid (pg 439) apothem (pg 610) geometric probability (pg 622) irregular figure (pg 617) irregular polygon (pg 618)
Geometry Ch 8 Quadrilaterals & Ch 11 Areas of Polygons and Circles Sec 8-1 Angles of Polygons How do you find what all the angles inside of a polygon add up to? Method #1: Every triangle has 180 degrees with all the angles added. You can break shapes into triangles and then add up all the 180 s. Method #2: Plug the number of sides in for n into the formula: (n 2)180 and calculate. What is an exterior angle? What is the sum of ALL exterior angles?
Sec 8-2 Parallelograms What is the difference between Quadrilaterals and Parallelograms? In a parallelogram, tell me what you know about a) The sides b) The angles c) The consecutive angles d) The diagonals
Sec 8-3 Tests for Parallelograms How can you test to see if a quadrilateral is a parallelogram? 1. Are both pairs of opposite sides parallel? 2. Are both pairs of opposite sides congruent? 3. Are both pairs of opposite angles congruent? 4. Do the diagonals bisect each other? 5. Are the consecutive angles supplementary? Using coordinates to prove a shape is a parallelogram. Prove A(-3, 0), B(-1, 3), C(3, 2), D(1, -1) is a parallelogram Method #1 Method #2 (Find slopes and (Find distance of each side prove opposite sides and prove opposite sides are parallel.) are equal.)
Sec 8-4 Rectangles What are some properties of rectangles? 1. Opposite sides are congruent and parallel. 2. Opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals are congruent AND bisect each other. 5. All four angles are RIGHT angles. Solving using rectangle properties In rectangle LMNP, draw in diagonals MP and NL and label <MLN = 5x + 8, <NLP = 3x + 2, and <MNL = 6y + 2. Find x AND y. Using coordinates to prove a shape is a rectangle. Prove whether Quadrilateral ABCD is a rectangle or not. A(-2, 1), B(4, 3), C(5, 0), and D(-1, -2). (Find the SLOPES and prove they have opposite signs & reciprocal slopes which proves they make 90 degrees.)
Sec 8-5 Rhombi and Squares Properties of a Rhombus. 1. A rhombus has ALL the properties of a parallelogram. 2. All equal sides. 3. Opposite angles are equal. 4. The diagonals are perpendicular. 5. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. 6. Each diagonal of a rhombus bisects a pair of opposite angles. Properties of a Square. 1. A square has ALL the properties of a parallelogram. 2. A square has ALL the properties of a rectangle. 3. A square has ALL the properties of a rhombus.
Sec 8-5 Rhombi and Squares In rhombus LMNP, draw in diagonal MP and LN and they intersect at Q. a) If <NQM =, find y. b) Find m<pnl if m<mlp = 64. Using coordinates to prove a shape is a rectangle. Determine whether parallelogram ABCD is a rhomus, a rectangle, or a square for A(-2, -1), B(-1, 3), C(3, 2), and D(2, -2).
Sec 8-6 Trapezoids Types of Trapezoids Properties of trapezoids 1. The base sides are parallel. Properties of isosceles trapezoids 1. Both pairs of base angles (the top pair and the bottom pair) of an isosceles trapezoid are congruent. 2. The diagonals of an isosceles trapezoid are congruent. 3. The two legs are congruent. Median of a trapezoid
Sec 8-6 Trapezoids Solving using properties of trapezoids DEFG is an isosceles trapezoid with median MN. Find DG if EF = 20 and MN = 30. (EF and DG are the parallel sides.) Using the same trapezoid above, find <D, <G, <E and <F if m<d = 3x + 5, and m<e = 6x 5. Using coordinates to prove a shape is a trapezoid or isosceles trapezoid. ABCD is a quadrilateral with vertices A(5, 1), B(-3, -1), C(-2, 3), and D(2, 4). Prove whether this shape is a trapezoid or an isosceles trapezoid.
Quadrilateral Summaries
Sec 11-1 Areas of Parallelograms Area of Parallelograms formula Example of finding the area AND perimeter of a parallelogram. Using coordinates to prove a shape is a square, rectangle or a parallelogram. The vertices of a quadrilateral are at A(-2, 3), B(4, 1), C(3, -2), and D(-3, 0). Find the area of the quadrilateral.
Sec 11-2 Areas of Triangles, Trapezoids, and Rhombi Area of a Triangle Area of a Trapezoid Area of a Rhombus
Sec 11-2 Areas of Triangles, Trapezoids, and Rhombi Using coordinates to find area. Find the area of trapezoid RSTU with vertices R(4, 2), S(6, -1), T(-2, -1), and U(-1, 2). Find the area of rhombus MNPR with vertices at M(0, 1), N(4, 2), P(3, -2), and R(-1, -3).
Sec 11-3 Areas of Regular Polygons and Circles Area of Regular Polygons (Area = ½ x apothem x perimeter) Area of a Circle Find the area Find the area of a regular pentagon with a perimeter of 90 meters.
Sec 11-3 Areas of Regular Polygons and Circles Find the area of the shaded section Find the area of the shaded region. Find the area of the regular hexagon.
Sec 10-1 Circles and Circumferences What is the difference between the radius and diameter of a circle? Find the Circumference and the Area of the circle.
Sec 10-2 Angles and Arcs What is a central angle? What is the sum of all central angles in a circle? What is the arc length? What is the area of a sector? Find the circumference AND the area of the sector.
Sec 11-4 Areas of Irregular Figures Find the areas of these irregular shapes. (Break them into simpler and more familiar shapes.) *You will NEED to know your special right triangles & Pythagorean Theorem to help solve many of these areas.
Sec 11-5 Geometric Probability Multi-step irregular areas (Topics include SohCahToa, Special Right Triangles, Geometric Means, Pythagorean Theorem, Law of Sines & Law of Cosines.)
Sec 11-5 Geometric Probability (continued ) Multi-step irregular areas (Topics include SohCahToa, Special Right Triangles, Geometric Means, Pythagorean Theorem, Law of Sines & Law of Cosines.)
Geometry Chapter 8 & 11 Study Guide Section 8-1 Angles of Polygons What is the Interior Angle Sum Theorem? What is the Exterior Angle Sum Theorem? How many sides does a triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon and decagon have? Section 8-2 Parallelograms Can you use the area of a parallelogram formula? Do you know the properties of a parallelogram? (Which sides are equal? Which angles are equal? Do the diagonals bisect each other? Do the diagonals meet at a perpendicular angle?) Section 8-3 Tests for Parallelograms What are some tests you can do to see if a quadrilateral is a parallelogram? What is the slope formula? What is the distance formula? Section 8-4 Rectangles Can you use the area of a rectangle formula? Do you know the properties of a rectangle? (Which sides are equal? Which angles are equal? Do the diagonals bisect each other? Do the diagonals meet at a perpendicular angle?)
Section 8-5 Rhombi and Squares Can you use the area of a Rhombi formula? Can you use the area of a Square formula? Do you know the properties of a rhombi? (Which sides are equal? Which angles are equal? Do the diagonals bisect each other? Do the diagonals meet at a perpendicular angle?) Do you know the properties of a square? (Which sides are equal? Which angles are equal? Do the diagonals bisect each other? Do the diagonals meet at a perpendicular angle?) Section 10-1 Circles and Circumference Do you know the difference between a radius and a diameter? Can you use the circumference of a circle formula? Can you use the area of a Square formula? Section 10-2 Angles and Arcs Do you know the sum of all central angles in a circle? Can you use the arc length of a circle formula? Can you use the sector area of a circle formula? Sec 11-1 Areas of Parallelograms Can you use the area of a parallelogram formula? On a coordinate grid, how can you prove two lines meet at a 90 degree angle? On a coordinate grid, how can you prove two lines are the same length?
Section 11-2 Areas of Triangles, Trapezoids, and Rhombi Can you use the area of a triangle formula? Can you use the area of a trapezoid formula? Can you use the area of a rhombi formula? Section 11-3 Areas of Regular Polygons and Circles Can you use the area of regular polygons formula? Can you use the area of a circle formula? Section 11-4 Areas of Irregular Figures Can you find the area of an irregular figure by breaking it into smaller known shapes? Section 11-5 Geometric Probability Can you use the formula for geometric probability? Formulas that are fair to use in a geometric probability question: all area formulas (listed above) special right triangles Pythagorean theorem geometric mean SohCahToa Law of Sines Law of Cosines
CSI Geometry: Area Learning Targets Scene Scene 1 Scene 2 Scene 3 Scene 4 Scene 5 Calculating Areas of Polygons and Circles Area Dissection Area of Irregular Figures Geometric Probability Earned Points Possible Points What is being scored? 5 pts Write out the general area equation, plug the numbers in and calculated the area correctly. 2 pts Showed all your work and found the area of The QUAD. 2 pts Showed all your work and found the area of The PENTA. 2 pts Showed all your work and found the area of The HEX. 2 pts Showed all your work and found the area of The OCTO. 2 pts Answered the question Which gives you the most scrumptious pizza for your dollar? correctly. 2 pts Broke the shape up into smaller familiar shapes that you can find the area of. 2 pts Wrote formula, plugged in numbers and found area of shape #1. 2 pts Wrote formula, plugged in numbers and found area of shape #2. 2 pts Wrote formula, plugged in numbers and found area of shape #3. 2 pts Wrote formula, plugged in numbers and found area of shape #4. 2 pts Answered the question Which area is the closest approximation? correctly. 5 pts Wrote out the formula, plugged in numbers and found the probability the spinner landed on the Shedd Aquarium correctly. 2 pts Showed your work and found the area of the court. 2 pts Showed all your work and found the area of all the triangles. 2 pts Showed all your work and found the probability of Armstrong making the shot. 2 pts Showed all your work and found the area of all the rectangles. 2 pts Showed all your work and found the probability of Grant 2 pts 2 pts 2 pts 2 pts 2 pts making the shot. Showed all your work and found the area of all the trapzoids. Showed all your work and found the probability of Harper making the shot. Showed all your work and found the area of all the circles. Showed all your work and found the probability of KukoC making the shot. Answered the question Which player has the lowest probability? correctly. Done?
Scene 6 Cryptic Puzzle Solver Text Message Case Summary 2 pts 2 pts 2 pts 2 pts 2 pts 2 pts 2 pts 2 pts 2 pts 4 pts 5 pts 5 pts 5 pts 5 pts Showed your work and found the area of the entire park correctly. Showed your work and found the area of the white circle parts correctly. Showed your work and found the area of the white shape in the top, right corner correctly. Showed your work and found the area of the triangle parts correctly. Showed your work and found the area of the parallelogram parts correctly. Showed your work and found the area of the trapezoid parts correctly. Showed your work and found the area of the walkway parts correctly. Answered the question Which is the closest approximation for the amount of grassy space? correctly. Plugged numbers in correctly. Showed and EXPLAINED your work and came out with the correct answer and who is our criminal. Prepare a typed case in which you need to demonstrate your understanding of each of the following topics: Calculating Areas of Polygons and Circles (Find one example from this project and one example from your book. Explain HOW you did them BOTH.) Area Dissection (Find one example from this project and one example from your book. Explain HOW you did them BOTH.) Area of Irregular Figures (Find one example from this project and one example from your book. Explain HOW you did them BOTH.) Geometric Probability (Find one example from this project and one example from your book. Explain HOW you did them BOTH.) 6 pts What 6 vocabulary words and definitions were necessary throughout this project? Final Score