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Geometry
Essential Math 12
Mr. Morin
Name: ___________________________
Slot:
____
Triangles Review ____
Quadrilaterals ___
Regular Polygons ___
Polygons Diagonals ___
Triangles ‐ Review Triangle Types Picture Properties All triangles Equilateral Isosceles Scalene Right Angles Quadrilaterals Name Drawing Properties Parallelogram Rectangle Square Rhombus Kite Trapezoid Questions 1. State two (2) properties that would prove a quadrilateral is a parallelogram. 2. A given quadrilateral has the following properties:
 the opposite sides have equal length
 the measures of consecutive (or adjacent) angles are not equal
A) Draw the quadrilateral with these properties.
B) State the name of this quadrilateral. 3. Looking at his chocolate bar from a top view, Brian states that it looks like a rectangle. State two
properties of Brian’s chocolate bar that make it a rectangle. 4. Choose best answer.
A given quadrilateral has four sides of equal length. The quadrilaterals with this property are
a) all parallelograms
b) all trapezoids
c) all triangles
d) all trapezoids and all rhombuses
e) all rhombuses 5. Choose the best answer. a)
b)
c)
d)
the diagonals are equal
the consecutive angles are equal
the diagonals are perpendicular
the opposite angles are equal 6. Choose the best answer. If all sides of a 4-sided polygon are equal, then:
a) The adjacent angles are equal.
b) The quadrilateral is a square.
c) The diagonals intersect at 90º.
d) The diagonals do not bisect the interior angles of the quadrilateral. Regular Polygons (n‐gons) Name Drawing Central Angle Sum of Interior Angle Equilateral Triangle (3‐sided) Measure on One Interior Angle Square (4‐sided) Pentagon (5‐sided) Hexagon (6‐sided) Heptagon (7‐sided) Octagon (8‐sided) Nonagon (9‐sided) Decagon (10‐sided) Dodecagon (12‐sided) Questions
1. The sum of the interior angles of a polygon is 900°. Determine the number of sides of the polygon.
2. A building foundation has 8-sided regular polygon piles. Each pile has a radius of 12 inches.
Determine the width of a face of the polygon.
3. A coin is in the shape of a regular polygon with 11 sides. State the measure of a central angle in degrees. 4. A regular hexagon has a side length of 10 metres.
a. State the measure of angle A, the central angle, in degrees.
b. State the measure of the given diagonal in metres.
5. Given the following regular polygon:
a. Calculate the sum of the interior angles in the polygon
b. State the measure of each interior angle in the polygon. 6. Given a regular hexagon with centre C:
a. Determine the measure of the central angle of the hexagon.
b. Determine the length of side a. Justify your response. 7. Polygons (regular and irregular) are often used in construction, commercial, industrial, or artistic
applications.
Demonstrate one use of the various properties of polygons in the real world by performing the
following two steps:
a. State a specific example where the various properties of polygons are used. Support your
example with a written explanation, or with other information or evidence, of how the various
properties of polygons are used.
b. Sketch a reasonably neat picture or diagram (not necessarily to scale) that supports your example
in Part A. Diagonals – Polygons 3
2
Name Drawing Formula Equilateral Triangle (3‐sided) Square (4‐sided) Pentagon (5‐sided) Hexagon (6‐sided) Heptagon (7‐sided) Octagon (8‐sided) Nonagon (9‐sided) Decagon (10‐sided) Dodecagon (12‐sided) Determine the number of diagonals in a regular octagon.
Determine (by illustration or calculation) the total number of diagonals in a regular six‐sided polygon. Draw a hexagon. a) Draw the diagonals of an octagon b) Verify the number of hexagon by the formula