Geometric Reasoning
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
GM4-5: Identify classes of two and three dimensional shapes by their geometric properties.
GM4-7: Communicate and interpret locations and directions, using compass directions, distances and grid references.
GM5-5: Deduce angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
GM -10: Apply Pythagoras' theorem in two dimensions.
GM4-5: Identify classes of two and three dimensional shapes by their geometric properties.
GM4-7: Communicate and interpret locations and directions, using compass directions, distances and grid references.
GM5-5: Deduce angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
GM -10: Apply Pythagoras' theorem in two dimensions.
In this unit you will learn:
- Naming and measuring angles
- Types of angles
- How to measure using a protractor
- Special pairs of angles
- Identify different triangles
- Quadrilaterals
- Angle sums of triangles and quadrilaterals
- Bearings
- Calculating angles on parallel lines
- Pythagorean Theorem
1) Naming and Measuring Angles
An angle is formed when two lines called arms meet at a point called a vertex. When naming angles, three letters are usually used. The letters are positioned at the end points of the arms.
Angles can be measured manually with a protractor.
2) Types of Angles...angles are classified according to their size.
3) How to Measure using a Protractor.
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4) Special Pairs of Angles.
Angles can be named by the way they are positioned in terms of another angle. Depending on the locations of each angle in the pair, they may have a mathematical relationship. Explore three different relationships:
- Divide a right angle in two to form two complementary angles which sum to 90 degrees.
- Divide a straight angle in two to form two supplementary angles which sum to 180 degrees.
- Cross two lines or segments to form two pairs of equal vertically opposite angles.
5) Triangles
Triangles can be described by considering side lengths and internal angles. Sides that have the same length are marked with similar dashes and equal angles are indicated with the same markings.
Triangles are classifies by their internal angles. An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and twoacute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle.
6) Quadrilaterals
All four-sided two-dimensional shapes are quadrilaterals. Quadrilaterals are described according to their properties of their sides and angles, in a similar way to the way in which triangles are described.
- sides that are equal in length are shown with the same number of small dashes.
- sides marked with the same number of arrow heads are parallel.
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7) Angle Sums of Triangles and Quadrilaterals
8) Bearings
9 Calculating Angles on Parallel Lines
10) Pythagorean Theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
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Check out these cool sites...
https://www.youtube.com/user/LearnCoach
http://www.mathsisfun.com/angle180.html
http://www.mathsisfun.com/geometry/complementary-angles.html
http://www.mathplayground.com/alienangles.html
http://www.bbc.co.uk/bitesize/ks2/maths/shape_space/angles/play/popup.shtml
https://www.goconqr.com/en-US/flashcard/9643508/Year-9-Angle-Rules-and-Terms
http://www.mathsisfun.com/angle180.html
http://www.mathsisfun.com/geometry/complementary-angles.html
http://www.mathplayground.com/alienangles.html
http://www.bbc.co.uk/bitesize/ks2/maths/shape_space/angles/play/popup.shtml
https://www.goconqr.com/en-US/flashcard/9643508/Year-9-Angle-Rules-and-Terms