Geometry
Grade 7/8
Curriculum Expectations
Grade 7
I will be able to:
- construct related lines,
-sort and classify triangles by geometric properties related to symmetry, angles and sides
– construct angle bisectors and perpendicular bisectors, using a variety of tools
– identify, through investigation, the minimum side and angle information
– determine, through investigation using a variety of tools relationships among area, perimeter, corresponding side lengths, and corresponding angles of congruent shapes
-demonstrate an understanding that enlarging or reducing two-dimensional shapes creates similar shapes
-distinguish between and compare similar shapes and congruent shapes, using a variety
of tools and strategies
Grade 8
I will be able to:
By the end of Grade 8, students will:
-sort and classify triangles by geometric properties, including those based on diagonals.
-construct a circle, given its centre and radius, or its centre and a point on the circle, or three points on the circle
-investigate and describe applications of geometric properties (e.g., properties of triangles, quadrilaterals, and circles) in the real world.
-determine, through investigation using a variety of tools, relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes
-determine, through investigation using a variety of tools and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle
-solve angle-relationship problems involving triangles (e.g., finding interior angles
or complementary angles), intersecting lines (e.g., finding supplementary angles or
opposite angles), and parallel lines and transversals (e.g., finding alternate angles
or corresponding angles)
-determine the Pythagorean relationship, through investigation using a variety of
tools (e.g., dynamic geometry software; paper and scissors; geoboard) and strategies;
– solve problems involving right triangles geometrically, using the Pythagorean
relationship;
Minds On...
What are examples of shape properties?
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What are you able to express about properties of different shapes?
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Action...
Do you agree with the conjecture that triangles with the same area must be congruent? Justify your reasoning.
Consolidate
Copy the note in your math notebook.
Important Terms in Geometry
Point - identifies a position. A point has no size. A dot is used to represent a point, and a capital letter is used to name it.
Line - is a straight path of points with no endpoints. It extends forever in both directions. A line is named by using any two points on the line or with a single lower case letter.
Ray - a part of a line. A ray starts at one endpoint and extends forever in one direction.
Line Segment - is a part of line and has two endpoints.
Angle - formed by two rays or line segments with a common endpoint, called the vertex. The rays or line segment are the arms or sides of the angle.
Constructing Triangles
Bisecting an Angle
Dilatations
Dilatation Assignment
Using a picture of your choice, your task is to dilate your photo using a scale factor greater than 1.
Step 1: Choose a picture, drawing, logo, or photo from a magazine.
Step 2: Have your teacher photocopy your drawing.
Step 3: Glue your photo/drawing onto the grid paper, and extend the grid lines onto your photo.
Step 4: Determine your scale factor. Re-draw your photo using larger grid paper, or simply draw in your new scale factor on your grid paper.
See the example below: