 Download Download Presentation Geometry in Nature and in Art

# Geometry in Nature and in Art

Download Presentation ## Geometry in Nature and in Art

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript

1. Geometry in Nature and in Art Day 2 (8/21/2012) Assignment Class work Decorate the folder using designs on page 8,10, 11, and 35* Identify reflectional or rotational symmetry of your design. Homework Read lesson 1.1 Page 28 Objectives: • Use geometry to create art designs. • Identify reflectional and rotational symmetry.

2. Section 1.1 Building blocks of Geometry Day 3 (8/22/2012) Assignment Class Work Finish the Folder design. (15 min) Take notes from the LCD on definitions. Work on the Investigation on page 32. Homework Page 33 # 1-15 all Objectives: • Learn the terminology and the notation of points, lines, segments, rays, plane, collinear and coplanar points.

3. Section 1.1 Building blocks of Geometry Day 4 (8/23/2012) Assignment Class Work Go over homework questions. Homework Page 34 # 18-35 all Objectives: • Learn the terminology and the notation of points, lines, segments, rays, plane, collinear and coplanar points.

4. Warm-up Day 4 Graph each point: • A(0,-2), B(-1,2), C (3,0), D(-1,-3) Graph and name: • The line that passes through A and B. • The line segment that passes through D and C. • The ray with initial point C and passes through A.

5. Section 1.1 Midpoint Day 5 (8/24/2012) Assignment Class work Warm-up (5 min) LCD Power Point presentation. Page 37 # 1-8 all Homework: Read section 1.2 Page 38. Objectives: • Review coordinate midpoint property. • Find the coordinates of the midpoint by using midpoint formula.

6. Section 1.2 Poolroom Math Day 6 (8/28/2012) Assignment Class Work LCD lectures Go over Examples B and C page 40-41. Go over page 42-43 # 1, 2, 15, 16, 20. Homework Page 42-43 # 1-25 all. Objectives: • Definition of a angle. • Learn how to show the measure of an angle. • Become familiar with the symbols of marking angles and congruent angles.

7. Section 1.2 Poolroom Math Day 7 (8/29/2012) Assignment Class Work: Collect homework day 4. Page 44-45 # 31-40 all. Homework : Review Concept and notation of sections 1.1-1.2. • Objectives: • Definition of a angle. • Learn how to show the measure of an angle. • Become familiar with the symbols of marking angles and congruent angles.

8. Warm- upDay 7 1. Find the coordinates of the midpoint of the segment with the given endpoints (5,8) and (3, 2). 2.Tell whether the statement below is sometimes, always, or never true. Support your answer with a sketch. If M is the midpoint of KL, then M, K, and L are collinear.

9. Definition: Angle Bisector • An angle bisector is a ray that divides an angle into two congruent angles. • JK bisects LJM; thus LJKKJM.

10. Example 1 • KM bisects JKL, mJKM= (4x + 6)°, and mMKL= (7x – 12)°. Find mJKM.

11. +12 +12 Example 1 Continued • Step 1 Find x. mJKM = mMKL Def. of  bisector (4x + 6)° = (7x – 12)° Substitute the given values. Add 12 to both sides. 4x + 18 = 7x Simplify. –4x –4x Subtract 4x from both sides. 18 = 3x Divide both sides by 3. 6 = x

12. Example 1 Continued • Step 2 FindmJKM. mJKM = 4x + 6 = 4(6) + 6 Substitute 6 for x. = 30 Simplify.

13. Quiz Day 8 (8/30/2012) Assignment Homework Read section 1.3 • Objectives: • Quiz on section 1.1-1.2

14. Section 1.2 Day 8 (8/30/2012) Assignment Class Work Go over the warm up. Quiz (30 min ) Homework Read section 1.3 • Objectives: • Understand the definition of angle bisector. • Use the definition of the angle bisector to find the missing side.

15. Section 1.3 Day 9 (8/31/2012) Assignment Class work Go over the worm up Go over the quiz Go over example B on page 48. Go over the investigation on page 49. Homework Learn the definitions of special angles. • Objectives: • Review section 1.1-1.2 concepts. • Practice to write definitions. • Define special angle relationship.

16. Warm- up Day 9 (8/31/2012) • 1. Copy the figure. Write what you know about the markings. N R Q P M

17. QS bisects PQR, mPQS= (5y – 1)°, and mPQR= (8y + 12)°. Find mPQS. Warm up 1. Find the measure of each angle. 2. JK bisects LJM, mLJK= (-10x + 3)°, and mKJM= (–x + 21)°. Find mLJM.

18. Section 1.3 Day 10 (9/4/2012) Assignment Class Work Go over the warm up. Go over investigation “ Definition of angles” on page 49. Homework Page 51 -52 # 1-8 all, 11, 13. • Objectives: • Practice to write definitions. • Define special angle relationship.

19. Warm-up Day 10 1. Eis between D and F. Find DF. 2. Dis the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E F 4x + 6 D 7x – 9

20. Section 1.3 Day 11 (9/5/2012) Assignment Class Work Go over the Warm up Go over the homework. Go over examples from the hand out. Homework Finish the hand out Objectives: Use the definition of special angles to find the missing angle or solve for X.

21. Warm up Day 11 • mA= 60, and mB=70. Find the measure of each of the following. • 1. supplement of A • 2. complement of B • 3. Determine whether this statement is true or false. If false, explain why. If two angles are complementary and congruent, then the measure of each is 90°.

22. Section 1.3 Special angels Day 12 (9/ 6/ 2012) Assignment Class Work Go over the Warm up Go over examples from the Hand out. Homework Finish the hand out and review for the quiz. Objectives: • Review sections 1.1-1.3

23. Warm up Day 12 1. Name the pairs of vertical angles. 2. mXYZ = 2x° and mPQR= (8x - 20)°. If XYZ and PQR are supplementary, find the measure of each angle.

24. Answers to the homework of Day 11 • 2. 70/3 • 3. x = 10 and m<ABC = 52 • 8. x = 30 and m<AOB = 30 • 9. x = 30 and m< BOC = 120 • 10. x = 20 and m< BOC = 40 • 11. x = 8 • 12. y = 35 • 13. 35 • 14. LM= 20, MN = 3 • 15. m< COB = 61, m< BOA = 29

25. Quiz on Sections 1.1-1.3 Day 13 (9/7/2012) Assignment Class Work Finish the Review hand out. Quiz Homework: Read section 1.4 page 54- 55. • Objectives: • Test concepts of sections 1.1-1.3.

26. Section 1.4 Polygons Day 14 (9/10/12) Assignment Class Work Go over the warm up. Go over the vocabulary of section 1.4. Homework Page 57 # 1-12 all 15, 21, 22. Objectives: • Define and classify polygons and related terms. • Practice writing definitions. • Learn even more vocabulary.

27. Day 14 Warm up Identify each of the following. • 1.points that lie in the same plane • 2. Two angles whose sum is 180° • 3. Two lines that never meet. • 4. An angle that is less than 90 degree.

28. Day 14 Vocabulary • Polygon • Diagonal • Convex • Concave • Congruent polygons • Perimeter • Equilateral Polygon • Equiangular Polygon • Regular Polygon

29. Vocabulary Day 14 1. Polygon • A polygon is a closed figure, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. 2. Diagonal • Diagonal of a polygon is a line segment that connects two nonconsecutive vertices. 3. Convex Polygon • A polygon is convex if no diagonal is outside of the polygon . 4. Concave Polygon • A polygon is concave if at least one diagonal is outside of the polygon. 5. Congruent Polygons • If polygons are congruent, then corresponding sides and angles are congruent OR If corresponding sides and angles are congruent, then the polygons are congruent. 6. Perimeter The perimeter of a polygon is equal to the sum of the lengths of its sides.

30. Vocabulary Continues….. 7. Equilateral Polygon • Equilateral polygons are polygons in which all sides have equal length. 8.Equiangular Polygons • Equiangular polygons are polygons in which all angles have equal measure. 9. Regular Polygons • Regular polygons are polygons that are both equilateral and equiangular.

31. Section 1.4 Polygons Day 15 (9/11/2012) Assignment Class Work Collect Homework day 14. Go over the warm- up Go over the quiz. Homework Page 58 23-25 all. Objectives: • Define and classify polygons and related terms. • Practice writing definitions. • Learn even more vocabulary

32. Day 15 Warm up Classify each angle as acute, obtuse, or right. • 1.2. • 3. 4. If the perimeter is 47, find x and the lengths of the three sides.

33. Section 1.4 Polygons Day 16 9/12/2012 Assignment Class Work Quiz make up Hand-out. Homework Finish the hand-out Objectives: • Test concepts of sections. 1.1-1.4

34. Section 1.4 Polygons Day 17 9/13/2012 Assignment Class Work Go over the warm up. Go over the homework questions. Finish the hand-out. Homework Read section 1.5 find a definition and write an example for each bolded term. Objectives: • Review definition of a polygon and related terms. • Use the definition to solve problems.

35. Section 1.5 Triangles Day 18 (9/14/2012) Assignment Class work Go over the warm up Go over the homework questions. Note book quiz. Homework Page 62 # 1-9 all, page 63 17-21 all. Objectives: • Define and classify triangles • Practice with definitions.

36. Warm up day 18 Define the following terms. • Right triangle • Equilateral triangle • Obtuse triangle • Collinear Points

37. Vocabulary Day 18 Right triangle • A right triangle has a right angle. Acute triangle • An acute triangle has three acute angles Obtuse triangle • An obtuse triangle has one obtuse angle. Scalene triangle • A scalene triangle is a triangle with no congruent sides. Equilateral triangle • An equilateral triangle has three congruent sides. Isosceles triangle. • An isosceles triangle has at least two congruent sides.

38. Section 1.5 Triangles Day 19 (9/18/2012) Assignment Class Work Go over the Warm up. Go over homework Questions. Hand out 1-9 All Homework Defined the bolded terms on section 1.6 • Objectives: • Define and classify triangles • Practice with definitions. • Use the definitions of sections 1.2-1.5 to answer hand out questions.

39. Warm up Day 19 1. Classify EHF by its side lengths. 2. Find the side lengths of equilateral FGH.

40. Warm up Day 20 • Classify each triangle by its angles and sides. • 1. MNQ • 2.NQP • 3. MNP

41. Warm up Day 20 Answers • Classify each triangle by its angles and sides. • 1. MNQ • 2.NQP • 3. MNP acute; equilateral obtuse; scalene acute; scalene

42. Section 1.6 Special Quadrilaterals. Day 20 (9/19/2012) Assignment Class Work Go over the warm up Go over homework questions. Write definitions of the bolded terms. Homework Page 66 # 1-13 all. Objectives: • Define and classify quadrilaterals along with their related parts. • Learn more vocabulary related to quadrilaterals.

43. Vocabulary Day 20 1. Trapezoid • A trapezoid is a quadrilateral with exactly one pair or parallel sides. 2. Kite • A kite is a quadrilateral with two distinct pair of consecutive congruent sides. 3. Parallelogram • A parallelogram is a quadrilateral with two pairs of parallel sides. 4. Rhombus • A rhombus is an equilateral parallelogram 5. Rectangle • A rectangle is a equiangular parallelogram. 6. Square A square is a regular quadrilateral .

44. Section 1.7 Special Quadrilaterals. Day 21 (9/20/2012) Assignment Class Work Go over the warm up. Collect Homework day 20. 30 min Quiz on section 1.6-1.7. Homework Hand out page 6. Objectives: • Learn more vocabulary related to quadrilaterals • Use the definitions of this section to solve problems.

45. Warm up Day 21 For 1-3 , draw and label each figure. • An obtuse triangle ABC with obtuse angle <A. • An isosceles right triangle KLM with KL=KM and m<K=90. • A Kite ABCD with AB=3cm, BC=3cm, CD=6 cm, and AD= 6 cm. • If KL=5 in, what is the perimeter of a regular polygon KLMNP.

46. Section 1.7 Circles Day 22 (9/21/2012) Assignment Class Work Go over the warm up Defined the circle and parts of a circle. Start working on the homework Homework: Page 72 # 2-9 all, 11, 23-26 all. 29, 30, 34. Objectives: • Define a circle and related figures. • Identify parts of a circle.

47. Warm up Day 22 1. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

48. Vocabulary of section 1.7 1. Circle • A circle is a set of points equidistant from a fixed point called the center. 2. Chord • A chord is a line segment whose end points lie on the circle. 3. Diameter • A diameter is a chord that passes through the center. The diameter is the longest cord. 4. Tangent • A tangent is a line that intersects the circle only once.

49. Vocabulary 1.7…. 5. Arc • An arc is made of two points on the circle and the continuous (unbroken) part of a circle between the two points. The two points are called the end points. 6. Semicircle • Is the arc of the circle whose endpoints are the end points of a diameter. 7. Minor Arc • A minor arc is an arc that is smaller than a semicircle. 8. Major Arc • A major arc is a arc that is larger than the semicircle. Central angle • A angle whose vertex is the center of a circle.

50. Example 1. • Identify each term. Chords: Semicircle Tangent: Diameter: Radius: Minor arc: Major arc: