Specific Learner Expectations Space and Shape€¦ · • perpendicular line segments • parallel...

Grade 7 MathSpecific Learner Expectations

Space and Shape

1. bemonstrate an understanding of circles by:• describing the relationships among radius, diameter and

circumference• relating circumference to p1• determining the sum of the central angles• constructing circles with a given radius or diameter• solving problems involving the radii, diameters and circumferences

of circles.2. bevelop and apply a formula for determining the area of: triangles;

parallelograms; circles.3. Perform geometric constructions, including:

• perpendicular line segments• parallel line segments• perpendicular bisectors• angle bisectors.

4. Identify and plot points in the four quadrants of a Cartesian plane, usingintegral ordered pairs.5. Perform and describe transformations (translations, rotations or

reflections) of a 2-b shape in all four quadrants of a Cartesian plane(limited to integral number vertices).

TransformationsYou perform a transformation when you take a geometric shape andmove it according to specific rules, in order to recreate the shape in adifferent place or position.

We will be learning about three specific types of transformations:• translations (slides)• rotations (spins)• reflections (flips)

Translations: a translation, or slide, is a motion that is described bylength and direction. The resulting shape has the same sense as theoriginal (same direction, orientation, size and shape).The slide can be named for the horizontal and vertical motion itundergoes.

For example

• a translation of (5, -2), moves the object 5 units to the right andtwo units down.• You could also call it (5R, 2b) for 5 right and 2 down.• A third way this can be named is based on the origin point (x + 5,y-2).• It is important to remember that the signs ‘+“ and “-s’ indicatethe direction you are moving the shape. Along the x axis, “+“

means to the right and “-“ means to the left. Along the y axis, “+“

means up and a—” means down. This corresponds to the quadrantson the Cartesian plane.

• A translation arrow shows the direction and the distance atranslation moves an object through.

Reflections: a reflection is a transformation in which a figure isreflected, or flipped over a mirror line or reflection line.

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Rotations: a transformation in which a figure is turned or rotatedabout a point, called the centre of rotation or the turn center.

Congruent: equal or exactly the same. When we transform a shapethrough translations, rotations and reflections, the resulting shapesare congruent to the original shapes.

Ordered pair: pairs of numbers that describe the location of a pointon the coordinate plane compared to the origin. The first number inthe pair represents the x coordinate (side to side), the secondrepresents the y (up and down) coordinate.

Origin: the point at which the x-axis and y-axis intersect; the originhas coordinates of (0,0)

Vertices: the points where line segments join to make a shape; thecorners of a shape.

Translation: a slide, or a motion that is described by length anddirection. The shape produced by a translation has the same sense asthe original, which means it looks exactly the same as the original, onlyin a different place (it has not been flipped or rotated, only moved).

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____________________

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Translation, Rotation, and Reflection

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Four Quadrant Ordered Pairs-—

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5) (-4,+7)

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6) (-8,+0)

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7) (-8,-7

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Write the ordered pair for each given point.9) K

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Plot the following points on the coorinate grid.17) B (-6,+8) 19) C (-2,-6 )18) I (-6,-7 ) 20) A (+5,-5)

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Plot the following points on the coorinate grid.17) V (-5,-7 ) 19) A (+7,+9) 21) H (+3,+4)18) I (-3,÷1) 20) Z (-4,-2 ) 22) K (+7-6)

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Connect each sequence of points with a line.(-3,0) , (-4,-i), (-6,-2), (-6,-3), (-5,4) , (-4,4), (-3-4), (1,-2) End of Sequence(-11), (5,3) (6,5) , (7,5), (7,3), (9,2) , (8,15) , (8,2) , (2,-.5) End of Sequence(-5,-3) , (-5.5,0) , (-5,0) , (-5,-6) , (-4.5,-6), (-5,-3) End of Sequence(-9,3) , (-7,4), (7,-3), (5,4), (-9,3) End of Sequence(-6,-2) , (-4,-3) , (-2,-2) , (-1,-i) End of Sequence(5,3) , (4,4) , (4.5,4.5), (5.5,4) End of Sequence(-4,-i) , (-2,-2) End of Sequence

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Four Quadrant Graphing PuzzteY

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Use what you know about transformations to answer the questions below. Draw your answers on thegrid.

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Translations (A)Draw the intermediate and translated images.

Translate by (0, 0).Translate by (-5, -5).

Translate by (-3, 2).Translate by (-5, -3).

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5. Reflect the triangle over the x-axis.

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Draw the following transformations based on the reflections and rotations of the shapes below. Note: Thetransformations are shown on the second page.

1. Draw a reflection of the figure shown over the xaxis.

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Reflections

1) Reflection: Across Line y — 2) Reflection: Across the x-axis

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Rotations

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1) Rotation: 900 clockwise about the originV

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3) Rotation: 90° clockwise about the origin

5) Rotation: 180° about the origin

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I) rotation 90° clockwise about the origin 2) rotation 1800 about the origin

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5) rotation 180° about the origin 6) rotation 90° clockwise about the origin

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Perpendicular Bisectors,, Parallel Lines and Angle Bisectors

Perpendicular Bisector: A line that crosses another line at a 900 angle

Parallel Lines: Lines that travel in the same direction and never intersect

Angle Bisector: A line that cuts through another line at a specific angle

Math 7 Notes9.6 Classifying Angles• Angles are named according to their size.

Angle Name Angle SizeAcute Less than 900Right 90°

Obtuse between 90° 180°Straight 180°Reflex between 180° & 360°

Complementary AnglesTwo angles are called complementary angles if the sum of their degreemeasurements equals 90 degrees. These two angles are complementary.

**Note that these two angles can be‘pasted” together to form a rightangle!

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58°

32°Supplementary AnglesTwo angles are called supplementary angles if the sum of their degreemeasurements equals 180 degrees. These two angles are supplementary.

**Note that these two angles can be ‘pasted’1 together to form a straight line!

139°

Math 7 Notes

9.7 Intersecting c& Perpendicular Lines

• Intersecting Lines - lines that cross each other.

A d Cb are Intersecting Lines

• When two lines intersect, pairs of opposite angles are formed.

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• Perpendicular Lines — two lines that intersect at right angles.

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Name:

Construct a perpendjcu bisector for each line segment.

Create a tine that is parallel using any method. Write down the method that you used.

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Grade 7 Math — 2D Geometry

Construct an angie bisector for each angle using a protractor:

Construct an angle bisector for each angle using a compass:

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