# AS 1.6 Geometric Reasoning AS91031

##### Summary: 4 Credit External Assessment

Angle properties of intersecting and parallel lines and properties of polygons.
Similar shapes & using proportion to find unknown side lengths.
Using pythagoras in 2 and 3 dimensions.
Using trigonometry in 2 and 3 dimensions.
Using angle properties relating to circles.

• Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
• Recognise when shapes are similar and use proportional reasoning to find an unknown length.
• Use trigonometric ratios and Pythagoras’ Theorem in two dimensions.
• Deduce and apply the angle properties related to circles. Starters Geogebra Java Manipulatives
 Overview and Basic Angle Rules   Review of Angles. Basic geometric rules: Angles on a line add to 180. Opposite angles are equal. Angles at a point add to 360. Angles in a triangle add to 180. Achievement Standard Overview | Class notes, Blank notes Overview | Measuring Angles | Angle rules 1 Opposite Angles | Angles on a line | Angles at a point Angles in Triangles  The sum of angles in triangles: scalene, isosceles, equilateral. Class notes, Blank notes Ex 31.01 p448 (Ex 31.02 p451) Angles in Triangles Angles in a triangle | Isosceles Triangle Parallel Lines   Corresponding Angles equal, Co-interior angles add to 180, Alternate angles are equal Class notes, Blank notes Parallel line rules Ex 31.03 p453 Practice Ex 31.04 p454 Harder Problems Ex 31.05 p456 Parallel Lines p128 Corresponding | Two Corresponding | Alternate | Cointerior Are Lines Parallel? Using parallel line rules to determine if lines are parallel Ex 31.06 p457 Polygons  Interior & exterior angles. Sum of Exterior angles in a polygon Sum of Interior angles in a polygon Class notes, Blank notes Ex 31.07 p461 Ex 31.08 p464 Polygons p129 Exterior Angles Quadrilaterals  Names and properties of quadrilaterals Describing quadrilateral properties Rotational Symmetry. Reflective Symmetry. Total order of symmetry Class notes, Blank notes Ex 32.01 p468 Rectangle | Finding angles in Quadrilaterals Solving angle problems involving quadrilateral properties Ex 32.02 p470 p130 Similar Triangles Definition of similar triangles. Solving problems involving similar triangles Class notes, Blank notes Ex 32.03 p473 p132 Similar Triangles Circles   Definitions of radius, diameter, chord, arc, sector, segment, circumference, tangent. Two radii form an isosceles triangle. Angle in a Semicircle is 90 Angle at centre is twice angle at circumference Class notes, Blank notes Circle parts Ex 33.01 p476 Circle angle problems Ex 33.02 p479 Isosceles triangle | Angle in a semicircle | Angle at centre Angles on Same Arc, Cyclic Quadrilateral  Proof of angles on same arc are equal. Opposite angles in a cyclic quadrilateral add to 180 Class notes, Blank notes Angles on Same Arc Ex 33.03 p481 Cyclic Quadrilaterals Ex 33.04 p483 p133 Angles on same arc | Cyclic Quadrilaterals Concyclic points Definitions of collinear, concyclic, circumference Class notes, Blank notes Ex 33.05 p476 p134 Circle Tangents Definitions of tangent. Tangent and radius are perpendicular Ex 33.06 p487 p135 Radius and tangent Using Algebra in Geometry Using geometric reasoning and algebra to solve problems. Class notes, Blank notes Ex 33.08 p490 p136 Geometric Proofs Using geometric reasoning to follow a chain of reasoning and solve problems. Class notes, Blank notes Ex 33.09 p491 p137 Geometry Terms Review of geometric rules and vocabulary Class notes, Blank notes Ex 31.08 p464 | Ex 33.07 p489 p127 Revision Practice assessments Class notes, Blank notes Practice test p494 p138