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GEOMETRY

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PLANE FIGURES A plane is a flat surface that goes on and on in all directions. A plane figure is a flat geometric shape. POLYGONS A polygon is a closed plane figure made up of three or more line segments (sides) that are connected.

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**vertices A vertex is the point where two sides of a polygon meet.**

The plural of vertex is vertices. vertices

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**Polygons are named by the number of sides they have.**

A triangle has 3 sides. A quadrilateral has 4 sides. A pentagon has 5 sides. There are also names for polygons with seven sides, nine sides, and any number of sides! A hexagon has 6 sides. An octagon has 8 sides.

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PERIMETER The perimeter of a figure is the distance around the outside. What is the perimeter of each of these polygons? 12 in. 8 units 6 in. 6 in. 9 units 9 units P = 36 in. P = 37 units 11 units 12 in. 15 m. 5 m. P = 39 m. 16 ft. 16 ft. 5 m. 4 m. P = 50 ft. 10 m. 18 ft.

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AREA The area of a flat surface is the number of square units needed to cover the surface. What is the area of each of these polygons? Count the square units to find out. A = 20 sq. units A = 104 sq. units

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AREA The area of a flat surface is the number of square units needed to cover the surface. What is the area of each of these rectangles? Multiply to find out. 4 units 4 units A = 8 x 13 = 104 sq. units A = 4 x 4 = 16 sq. units

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CIRCLES A circle is a closed curve that is made of points that are the same distance from the center. A line segment is a part of a line. A radius is any line segment that connects the center to a point on the circle. A diameter is any line segment that passes through the center of a circle, connecting two points on the circle. A diameter is twice as long as a radius.

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CIRCLES The circumference is the distance around a circle. The circumference of a circle is about 3 times the diameter. C = about 3 x d

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CIRCLES The area of a circle is the number of square units needed to cover the inside of the circle. Find the approximate area of a circle by counting the square units inside or by multiplying the radius times the radius times 3. A = about 3 x r x r

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**CIRCLES P = about ______ units. A = about ______ sq. units. 18 36 27**

Find the approximate perimeters of the circles below. R = 3 units R = 6 units P = about ______ units. A = about ______ sq. units. 18 36 27 P = about ______ units. A = about ______ sq. units. 108

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CONGRUENT FIGURES Congruent figures have the same size and shape.

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SIMILAR FIGURES Similar figures have the same shape. If they also have the same size, they are congruent.

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MOVING PLANE FIGURES A slide (translation) moves a figure up, down, or over.

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MOVING PLANE FIGURES A turn (rotation) rotates a plane figure.

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MOVING PLANE FIGURES A flip (reflection) is a mirror image of a figure.

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**SYMMETRY A plane figure has symmetry if its halves match.**

If a plane figure has symmetry, it can be folded so its halves match. The fold is called a line of symmetry.

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SYMMETRY How many lines of symmetry do each of these plane figures have?

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**TESSELLATIONS (TILING)**

A tessellation completely covers the inside space of a plane figure, usually in some kind of organized pattern.

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**Now use the tiles to experiment**

Now use the tiles to experiment. Which tiles will tessellate a piece of math paper? Try squares, triangles, hexagons, etc. Will circles tessellate a plane figure? Explain your answer.

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SOLID GEOMETRY A three-dimensional object is called a space figure or a solid. cube cylinder rectangular prism pyramid sphere cone

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**SOLID GEOMETRY VOCABULARY**

FACE pyramid rectangular prism cube sphere cylinder cone

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**SOLID GEOMETRY VOCABULARY**

VERTEX pyramid rectangular prism cube sphere cylinder cone

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**SOLID GEOMETRY VOCABULARY**

EDGE pyramid rectangular prism cube sphere cylinder cone

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**= one cubic unit 6 V = ______ cubic units**

The number of cubic units inside a solid is called the volume. 6 V = ______ cubic units

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**= one cubic unit 24 V = ______ cubic units**

The number of cubic units inside a solid is called the volume. 24 V = ______ cubic units

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**Count the cubic units to find the volume of this figure.**

SOLID GEOMETRY Count the cubic units to find the volume of this figure. V = ______ cubic units 22

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V = ______ cubic units 36

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**GEOMETRY VOCABULARY TERM EXAMPLE SAY A**

A point is an exact location in space. A point A A line is a collection of points that go on and on in both directions. It has no endpoints. C line BC A line segment is part of a line. It has two endpoints. line segment DE A ray is part of a line. It has one endpoint and continues on and on in one direction. F G ray FG Intersecting lines are lines that pass through the same point. line HK intersects line JI at point L Parallel lines are lines that never intersect. line JK is parallel to line BC. B BB D E H L I J K J K J K B C

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GEOMETRY VOCABULARY Two intersecting lines that form four right angles are perpendicular to each other. A C B D Line BC is perpendicular to line AD.

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**GEOMETRY VOCABULARY Two rays meet at a vertex, forming an angle.**

An angle that forms a square corner is a right angle. An angle greater than a right angle is an obtuse angle. An angle less than a right angle is an acute angle.

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