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Transcript
English for Maths I Week 5 Polygons The Heirarchy Polygons Triangles Quadrilaterals Trapezoid Kite Scalene Isosceles Isosceles Trapezoid Parallelogram Equilateral Rectangle Rhombus Square TASK 1. Say whether the following statements are true or false. ____________ An equilateral triangle is isosceles ____________ A square is a rectangle ____________ A rectangle is a square ____________ A square is a regular quadrilateral ____________ A square is a rhombus with a right angle ____________ If a kite has a right angle, then it must be a square. ____________ The base angles in an isosceles triangle are congruent. ____________ A parallelogram is a square. Task 2 Complete the handout “Properties of Polygons”. TASK 3 . Complete the following text on Polygons. 2-dimensional line segments star polygons derives from circuit corners a plane figure self-intersect In geometry a polygon is traditionally ………………..that is bounded by a finite chain of straight………………… closing in a loop to form a closed chain or ……………….. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or………………. The interior of the polygon is sometimes called its body. An n-gon is a polygon with n sides. A polygon is a………………. example of the more general polytope in any number of dimensions. The word "polygon"……………………. the Greek πολύς (polús) "much", "many" and γωνία (gōnía) "corner", "angle", or γόνυ (gónu) "knee".[1] The basic geometrical notion has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the bounding closed polygonal chain and with simple polygons which do not…………………, and they often define a polygon accordingly. A polygonal boundary may be allowed to intersect itself, creating…………………... Geometrically two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments may be considered parts of a single edge; however mathematically, such corners may sometimes be allowed. TASK 4. Work in groups of three to match the terms with their descriptions: Simple Curve Convex Closed Curve Simple Closed Curve Concave Polygons Does not cross itself and starts and stops at the same place. Simple and closed and have sides that are ONLY segments. Simple, closed, and has no indentations. (the segment connecting any two points in the interior of the curve is completely contained in the interior of the curve) Simple, closed, and has an indentation Does not cross itself, but it may have the same beginning and ending point Must start and stop at the same place Task 5. Work in groups of three to classify the following shapes for which the criteria hold true. Shape Simple Closed Polygon Convex TASK 5. Complete the missing information: Congruency: Two lines are congruent if they are the same ……………… Two angles are congruent if they have the same ………… AB CD ABC XYZ Concave TEST MOCK Definitions of Triangles and Quadrilaterals Definition A triangle with one right angle Shape Picture A triangle in which all angles are acute A triangle with one obtuse angle A triangle with NO congruent sides A triangle with at least 2 congruent sides A triangle with three congruent sides A quadrilateral with at least one pair of parallel sides A quadrilateral with two adjacent sides congruent and the other two sides also congruent A trapezoid with exactly one pair of congruent sides A quadrilateral in which each pair of opposite sides is parallel A parallelogram with a right angle A quadrilateral with all sides congruent A quadrilateral with four right angles and four congruent sides Example: Relationship between the number of sides and the number of diagonals in a polygon. Complete the following chart: Number of Sides Number of Diagonals 3 4 5 6 7 8 9 N TASK True or False? The number of diagonals in a figure is greater than the number of sides in that figure. – More About Angles TASK: Complete the missing terms below Two angles whose sum is 180° are called ______________________________________. Two angles whose sum is 90° are called ______________________________________. Vertical Angles are always congruent Transversal: A line that intersects a pair of lines in a plane Interior Angles: Exterior Angles: Alternate Interior Angles: Alternate Exterior Angles: Corresponding Angles: Theorem: If any two distinct coplanar lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent IF AND ONLY IF the lines are parallel. Example: In the following figure n || m. Explain why angles 1 and 2 are supplementary. N 1 2 M Example: Are the following lines parallel? n 40° 30° 70° m The sum of the measures of the interior angles of a triangle is _____________. Proof #1 (inductive reasoning) Tearing Paper Proof #2 (deductive reasoning) The Relationship between the sum of the Interior Angles and the sum of the Exterior Angles: Complete the following chart: Number of Sides in the polygon 3 4 5 6 Sum of the Measures of the Interior Angles Sum of the Measures of the Exterior Angles