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Geometry in My World

By Megan T

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Isosceles Right Triangle•This is a picture of the beams in my living room. Where they meet in the corner of the room creates an isosceles right triangle.•Theorem 51-1: Isosceles Triangle Theorem- if a triangle is isosceles, then its base angles are congruent.

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Line of Symmetry

•This is a picture of my living room fireplace. If you split the fireplace directly down the middle, there is a visible line of symmetry.•Line of symmetry- a line that divides a plane figure into 2 congruent reflected halves.

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Rectangular Prism

•This is a picture of a shoe box. It is a rectangular prism.•Prism-a polyhedron formed by 2 parallel congruent polygonal bases connected by lateral faces that are parallelograms.•V = Bh•S = L + 2B•L = ph

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Parallel Lines

•This is a picture of the beams on the ceiling of my living room. Each beam is parallel to the others.•Parallel lines- lines in the same plane that don’t intersect.•Theorem 5-7: Transitive Property of Parallel Lines- if 2 lines are parallel to the same line, then they are parallel to one other.

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Cylinder•This is a picture of many cylinders piled on each other. Each cylinder is a different size.•Cylinder- a 3-D figure with 2 parallel congruent circular bases and a curved lateral surface that connects the bases.•V = Πr2h•S = 2Πr2 + 2Πrh•L = 2Πrh

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Vertical Angles

•This is a picture of a light in my house. There are 2 lines intersecting that form vertical angles.•Vertical angle- the nonadjacent angles formed by 2 intersecting lines.•Theorem 6-4: Vertical Angle Theorem- if 2 angles are vertical angles, then they are congruent.

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Supplementry Angles

•This is a picture of drawers in my kitchen. The angles of each drawer are supplementary angles.•Supplementary angles- 2 angles whose measures have a sum of 180°.•Theorem 6-2: Congruent Supplements Theorem- if 2 angles are supplementary to the same angle or to congruent angles, then they are congruent

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Sphere•This is a picture of a soccer ball. A soccer ball is in the shape of a sphere.•Sphere- the set of points in space that are a fixed distance from a given point called the center of the sphere.

•V = 4/3Πr3

•S = 4Πr2

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Trapezoid•This is a picture of the corner of the door frame. The corner is shaped like a trapezoid.•Trapezoid- a quadrilateral with exactly one pair of parallel sides.•A = ½(b1 + b2)h

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Circle•This is a picture of a pot which is in the shape of a circle.•Circle- the set of points in a plane that are a fixed distance from a given point called the center of the circle.•C = 2Πr or C = Πd•L = 2Πr(m°/360°)•A = Πr2

•A(sector) = Πr2(m°/360°)

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Perpendicular Lines

•This is a picture of a window in my house. The window panes are perpendicular lines.•Perpendicular lines- lines that intersect at 90° angles.•Postulate 19: perpendicular Lines Theorem- if 2 non-vertical lines are perpendicular, then the product of their slopes is -1. Vertical and horizontal lines are perpendicular to each other.

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Obtuse Angle

•This is a picture of my ceiling in my house. It comes together to form an obtuse angle.• obtuse angle- an angle that measures greater than 90° and less than 180°.

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Points On A Plane

•This is a picture of my kitchen tablecloth. Each little square on it represents a point on a plane which is the tablecloth as a whole.•Theorem 4-1: if 2 lines intersect, then they intersect at exactly 1 point.•Theorem 4-2: if there is a line and a point not on the line, then exactly one plane contains them.•Theorem 4-3: if 2 lines intersect, then there exists exactly 1 plane that contains them.

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Same-Side Interior Angles•This is a picture of the railing of my stairs. The poles that connect to the railing create same-side interior angles.•Theorem 10-3: Same-Side Interior Angles Theorem- if 2 parallel lines are cut by a transversal, then the same-side interior angles are supplementary.

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45°-45°-90° Triangle

•This is a picture of a quilt. On the quilt are several 45°-45°-90° triangles.•Properties of a 45°-45°-90° Triangle: Side Lengths- in a 45°-45°-90° right triangle, both legs are congruent and the length of the hypotenuse is the length of a leg multiplied by √2.

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Complementary Angles

•This is a picture of a window in my house. The wood on the window makes complementary angles.•Complementary angles- 2 angles whose measures have a sum of 90°.•Theorem 6-1: Congruent Complements Theorem- if 2 angles are complementary to the same angle or to congruent angles, then they are congruent.

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Concave Polygon

•This is a picture of a star decoration. A star is a concave hexagon.•Concave polygon- a polygon in which a diagonal can be drawn such that part of the diagonal contains points in the exterior of the polygon.

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30°-60°-90° Triangle

•This is a picture of one of my stairs. The stair is a 30°-60°-90° triangle.•Properties of 30°-60°-90° Triangles- in a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the short leg, and the length of the longer leg is the length of the shorter leg times √3.

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Skew Lines•This is a picture of a tissue box. The tissue box has skew lines.•Skew lines- lines that are not coplanar and not parallel.

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Cone•This is a picture of a lamp shade. It is in the shape of a cone.•Cone- a 3-D figure with a circular base and a curved lateral surface that connects the base to a point called the vertex.•V = 1/3Bh•S = Πr2 + Πrl•L = Πrl