Exploring Polygons and Quadrilaterals on a Chinese Checkerboard

5. Problem of the Day How many different types of shapes can you make by connecting the holes on a Chinese checker board.

6. 1.4 Polygons p. 54-58

7. What is a Polygon? • A closed space figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. • Each line segment is called a ________ • Each endpoint where sides meet is a ________ of the polygon.

8. F D R N W A B C D E F K Consecutive Pieces • Consecutive angles • Consecutive vertices • Consecutive sides • To name a polygon the vertices must be listed in consecutive order. • Starting point is irrelevant • Order is extremely important

9. Diagonal • A line segment that connects two nonconsecutive vertices.

10. Types of Polygons • Convex Polygons • Has no diagonal with points outside the polygon • No “caves” • Concave Polygons • Has at least one diagonal with points outside the polygon • “caves”

11. Most Used Polygons Know these!

12. Congruent Polygons • Two polygons are congruent if and only if they are exactly the same size and shape. • Note: If and only if means a statement works in both directions. Which is not true of all statements. Example: If polygons are congruent then corresponding sides and angles are congruent. AND If corresponding sides and angles are congruent then polygons are congruent.

13. Other Classifications of Polygons • Equilateral • All sides have equal length. • Equiangular • All angles have equal measure. • Regular • Both equilateral and equiangular

14. Diagrams and Markings • In geometry we are rarely able to assume anything about a shape; however, there are a few things we are able to “assume”. • Things you can assume from a drawing: • Straight lines • Linear pairs • Vertical angles • Collinear pairs • Betweeness of points • Coplanarness

15. Diagrams and Markings • Things you canNOT assume from a drawing: • Measurement/size • Right angles/perpendicular lines • Parallel lines • Congruency • Midpoint

16. Locate, define and sketch: • Right Triangle - • Acute Triangle - • Obtuse Triangle - • Scalene Triangle - • Equilateral Triangle - • Isosceles Triangle – • Vertex of – • Legs of – • Base of – • Base angles of - Use pages 60-61 in your book!

17. Classifying Trianglesclassify by ANGLE and SIDES

18. Quadrilaterals • How many sides does a quadrilateral have? • 4 sides • What is the sum of the angle measures in a quadrilateral? • 360°

19. Locate, define and sketch: • Trapezoid – • Kite – • Parallelogram – • Rhombus – • Rectangle – • Square - Use pages 62-64 in your book!

20. Special Quadrilaterals • Parallelogram • A quadrilateral with BOTH PAIRS of opposite sidesparallel. • Rhombus • A parallelogram with four congruent sides. • Rectangle • A parallelogram with four right angles. • Square • A parallelogram with four congruent sides and four right angles.

21. Other Special Quadrilaterals • Kite • A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. • Trapezoid • A quadrilateral with exactly one pair of parallel sides.

22. Kite Parallelogram Trapezoid Rectangle Rhombus Isosceles Trapezoid Square The Relationships of Quadrilaterals Quadrilateral

23. Exercises • Based on the marks, what can you assume to be true in each figure? 2. 1.

24. Exercises For Exercises 3-8, sketch and label the figure. Mark the figures. • Isosceles acute triangle ACT with AC = CT • Scalene triangle SCL with angle bisector CM • Isosceles right triangle CAR with mCRA = 90° • Trapezoid ZOID with ZO || ID • Two different isosceles triangles with perimeter 4a + b

25. Exercises Determine the most precise name for each quadrilateral.

26. Problem of the Day How many different types of shapes can you make by connecting the holes on a Chinese checker board.

27. 1.6 Circles Pg 67-70

28. E A O D B C Circle Terms Center of Circle Diameter Radius Chord Tangent Point of Tangency

29. Types of Circles Cocentric Circles 8 cm 8 cm 3 cm Congruent Circles