Download Unit_5

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.
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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.