Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
History of geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Trigonometric functions wikipedia , lookup
Multilateration wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Unit 5 Geometry; Congruence, Constructions, and Parallel Lines Unit 5 serves as a transition to the geometry taught in seventh and eighth grades. More attention is given to notation conventions, the application of geometric properties, and the natural connections between geometry and algebra. Unit 5 has five main areas of focus: To classify and draw angles, To estimate the measure of angles with and without tools, To find angle measures and write equations by applying properties of orientations of angles and sums of angle measures in triangles and quadrangles, To identify and describe congruent figures; and to construct congruent figures using compass and straightedge, and To identify, describe, and sketch instances or reflections, translations, and rotations on a coordinate plane. Vocabulary Adjacent Angles – Two angles with a common side and vertex that do not otherwise overlap. Congruent – Figures that have exactly the same size and shape are said to be congruent to each other. Line of Reflection (mirror line) – A line halfway between a figure (preimage) and its reflected image. In a reflection, a figure is flipped over the line of reflection. Ordered Pair – Tow numbers, or coordinates, used to locate a point on a rectangular coordinate grid. The first coordinate x gives the position along the horizontal axis of the grid, and the second coordinate y gives the position along the vertical axis. The pair is written (x,y). Reflection (flip) – the flipping of a figure over a line (line of reflection) so its image is the mirror image of the original (preimage). Reflex Angle – An angle measuring between 180o and 360o. Rotation (turn) – A movement of a figure around a fixed point or an axis; a turn. Supplementary Angles – Two angles whose measures add to 180o. Supplementary angles do not need to be adjacent. 1 2 Translation (slide) – A transformation in which every point in the image is a figure is at the same distance in the same direction from its corresponding point in the figure. Informally called a slide. Vertical (opposite) Angles – The angles made by intersecting lines that do not share a common side. Vertical angles have equal measures. Games Angle Tangle – Student Reference Book, page 306 The purpose of this game is for students to practice estimating and measuring the size of angles. Spoon Scramble – Student Reference Book, page 333 Playing this game will give students practice at identifying equivalent expressions involving fractions. Frac-Tac-Toe (Decimal Version) – Student Reference Book, pages 314-316 Renaming fractions to decimals is the skill practiced in this game. Polygon Capture – Student Reference Book, page 330 Students will practice identifying properties of polygons. 3-D Shape Sort – Student Reference Book, page 335 Identifying the properties of 3-D shapes is the skill practiced in this game. Web Sites This web site has geometric flash cards for reviews on vocabulary terms: http://www.aplusmath.com/cgi-bin/flashcards/geoflash This is a good reference site for all kinds of information about geometry: http://www.coolmath.com/reference/geometry-trigonometry-reference.html This is a fun game called “Bathroom Tiles” that uses translations: http://www.bbc.co.uk/education/mathsfile/shockwave/games/bathroom.html Do-Anytime Activities To work with your child on the concepts taught in this unit, try these interesting and engaging activities: While you are driving in the car together, ask your child to look for congruent figures, for example, windows in office buildings, circles on stoplights, or wheels on cars and trucks. Look for apparent right angles or any other type of angles: acute,(less than 90o) or obtuse (between 90o and 180o). Guide your child to look particularly at bridge supports to find a variety of angles. Triangulation lends strength to furniture. Encourage your child to find corner triangular braces in furniture throughout your home. Look under tables, under chairs, inside cabinets, or under bed frames. Have your child count how many examples of triangulation he or she can find in your home.