Download English for Maths I

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