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Tuesday, March 4 Chapter13-4 Two Dimensional Figures

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Objective: To understand sides and angles of polygons.

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Two Dimensional Figures A polygon is a simple closed, two dimensional figure with three or more sides. The number of sides will determine a polygon’s name.

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Two Dimensional Figures When all of the sides and angles of a polygon are congruent, the polygon is a regular polygon. If the sides are not congruent, the polygon is irregular.

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Two Dimensional Figures A triangle has three sides and three angles. The inside angles of a triangle will always add to 180 °.

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Two Dimensional Figures Certain triangles have specific names: A scalene triangle has no congruent sides.

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Two Dimensional Figures Certain triangles have specific names: An isosceles triangle has two sides congruent.

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Two Dimensional Figures Certain triangles have specific names: An equilateral triangle has all sides congruent.

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Two Dimensional Figures A quadrilateral has four sides. The inside angles of a quadrilateral will always add to 360 °.

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Two Dimensional Figures Certain quadrilaterals have specific names: A rectangle has opposite sides that are congruent and parallel, and all angles are right angles.

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Two Dimensional Figures Certain quadrilaterals have specific names: A square has all sides that are congruent and parallel, and all angles are right angles.

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Two Dimensional Figures Certain quadrilaterals have specific names: A parallelogram has opposite sides that are congruent and parallel, and opposite angles are congruent.

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Two Dimensional Figures Certain quadrilaterals have specific names: A rhombus has all sides that are congruent, opposite sides are parallel and opposite angles are congruent.

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Two Dimensional Figures A pentagon has five sides. The inside angles of a pentagon will always add to 540 °.

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Two Dimensional Figures A hexagon has six sides. The inside angles of a hexagon will always add to 720 °.

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Two Dimensional Figures A heptagon has seven sides. The inside angles of a heptagon will always add to 900 °.

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Two Dimensional Figures A octagon has eight sides. The inside angles of a octagon will always add to 1080 °.

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Two Dimensional Figures A nonagon has nine sides. The inside angles of a nonagon will always add to 1260 °.

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Two Dimensional Figures A decagon has ten sides. The inside angles of a decagon will always add to 1440 °.

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Two Dimensional Figures The formula to find the sum of the inside angles of any polygon is the number of sides minus 2 then multiply by 180, or (n-2)180.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular quadrilateral (parallelogram) Since the polygon has 4 sides it is a quadrilateral. Since all sides are not congruent, it is irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular quadrilateral (parallelogram) Three of the inside angles add to 333˚. What is the remaining angle?

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular quadrilateral (parallelogram) Three of the inside angles add to 333˚. What is the remaining angle? 360˚ – 333˚ = 27˚

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. irregular hexagon Since the polygon has 6 sides it is a hexagon. Since all sides are not congruent, it is irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. irregular hexagon Five of the inside angles add to 685˚. What is the remaining angle?

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. irregular hexagon Five of the inside angles add to 685˚. What is the remaining angle? 720˚ – 685˚ = 35˚

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Regular quadrilateral (square) Since the polygon has 4 sides it is a quadrilateral. Since all sides are congruent, it is regular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (isosceles) How do we know two sides are congruent?

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (isosceles) Since the opposite angles are the same, the sides are the same length.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular pentagon Since the polygon has 5 sides it is a pentagon. Since all sides are not congruent, it is irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular pentagon Four of the inside angles add to 497˚. What is the remaining angle?

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular pentagon Four of the inside angles add to 497˚. What is the remaining angle? 540˚ – 497˚ = 43˚

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular.

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (scalene) Since the polygon has 3 sides it is a triangle. Since all sides are not congruent, it is irregular (scalene).

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (scalene) Two of the inside angles add to 129˚. What is the remaining angle?

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Two Dimensional Figures Identify the polygon and determine if it is regular or irregular. Irregular triangle (scalene) Two of the inside angles add to 129˚. What is the remaining angle? 180˚ – 129˚ = 51˚

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Two Dimensional Figures What do you say when you see an empty parrot cage?

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Two Dimensional Figures What do you say when you see an empty parrot cage? polygon

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Two Dimensional Figures Agenda Notes – Homework – Practice Skills 13-4 Due Wednesday, March 5 Chapter 13 Test Monday, March 10

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