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Geometric Reasoning

Discover the foundational concepts of geometric reasoning, including angles, lines, and various shapes such as triangles, circles, and polygons. This resource delves into properties of angles on straight lines, various triangle types, parallel line theorems, and the angle sums of polygons. Learn to apply past knowledge flexibly to solve geometric problems and explore the relationships between angles and shapes in geometry. Ideal for students and educators alike, this guide encourages critical thinking and metacognition in the study of geometry.

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Geometric Reasoning

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  1. Geometric Reasoning

  2. A Applying Past Knowledge 52° D B C 1. What can you find? LINES TRIANGLES PARALLEL LINES CIRCLES POLYGONS

  3. Thinking Flexibly B A D C 66o E G F 2. What can you find? ABE = CBF AD EG LINES TRIANGLES PARALLEL LINES CIRCLES POLYGONS

  4. P Q O 68 S R 3. What can you find? LINES TRIANGLES PARALLEL LINES CIRCLES POLYGONS

  5. G 135o Y F 52o X D A B 4. What can you find? LINES TRIANGLES PARALLEL LINES CIRCLES POLYGONS

  6. H G 214 J b° K L N 5. What can you find? GHKL is congruent to JHLN LINES TRIANGLES PARALLEL LINES CIRCLES POLYGONS

  7. Metacognition A x F K E B G J H C D 6. What can you find? LINES TRIANGLES PARALLEL LINES CIRCLES POLYGONS

  8. Angles on a straight line = 180 Straight Lines Angles at a point = 360 Vertices Vertically Opposite angles are equal Intersection of two straight lines Lines (and what to look for…) 1 2 3 4 5 6

  9. Triangles (and what to look for…) • Angle sum of a triangle = 180  • Triangle with two known angles • Exterior Angle of a triangle • Two internal angles of a triangle • Isoceles triangle base angles • One base angle in isos. Triangle • Angle sum of an isosceles triangle • One angle in isos. triangle 1 2 3 4 5 6 OR

  10. Parallel Lines (and what to look for…) • Corresponding angles • F • Alternate angles • Z • Co-interior angles • C 1 2 3 4 5 6

  11. Circles (and what to look for…) • Angles in a semi circle • Triangle using diameter of circle • Angles on the same arc • 4 connected chords • Angle at the centre • 2 chords connected to 2 radii • Isosceles triangle due to radii • 2 radii forming a triangle • Radius perpendicular to tangent • Tangent to circle 1 2 3 4 5 6

  12. Polygons(and what to look for…) • Angle sum of exterior angles = 360 • n-sided shapes with edges extended • Angle sum of interior angles = • n-sided shapes with interior angles 1 2 REGULAR SHAPES: IRREGULAR SHAPES: 3 4 5 6 REGULAR SHAPES: IRREGULAR SHAPES:

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