UNIT 8: THALES, PYTHAGORAS, AREA AND PERIMETERS (PLANE FIGURES)
CRITERIA:
1. Given the lengths of the three sides of a
triangle, to recognise whether or not it is right-angled.
2. To calculate the unknown side of a right-angled
triangle from the other two.
3. On a square or rectangle, to apply Pythagoras’s
theorem to relate the diagonal to the sides and calculate the unknown element.
4. On a rhombus, to apply Pythagoras’s theorem to
relate the diagonals to the side and calculate the unknown element.
5. On a right-angled or isosceles trapezium, to
apply Pythagoras’s theorem to establish a relation that makes it possible to
calculate an unknown element.
6. On a regular polygon, to use the relation between
the radius, apothem and side and, applying Pythagoras’s theorem, to find one of
these elements from the others.
7.To apply Pythagoras’s theorem in resolving simple geometry
problems.
8. To understand the concept of the similarity ratio and
apply it for the construction of similar figures and for the indirect
calculation of lengths.
9. To calculate the surface area of triangles,
quadrilaterals, regular and irregular polygons, circles and associated figures,
knowing the necessary data.
10. To calculate the surface area of triangles,
quadrilaterals, regular and irregular polygons, circles and associated figures,
previously calculating the data which is missing.
Contents
THALES THEOREM: Similarity criteria for triangles.
- Calculation of the height of an object indirectly, using similarity relation.
PYTHAGORAS’S THEOREM
• Relation between areas of squares.
• Applications of Pythagoras’s theorem.
– Calculation of one side of a right-angled triangle
knowing the other two.
– Calculation of a segment of a plane figure from
others which, with it, form a right-angled triangle.
– Identification of triangles and rectangles from the measurements of
their sides.
AREAS OF PLANE FIGURES
– Quadrilaterals: rectangles, squares, rhombuses,
trapeziums, etc.
– Triangles.
– Regular polygons.
– Circle and associated figures.RESOURCES:
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