Geometry in My World (MT)
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The document describes various geometric shapes and concepts that the author observed in her everyday life. It includes 21 examples from her living room, kitchen, and other areas of her house. Each example includes an image, name of the shape or concept, and relevant properties or definitions. The document uses real-world contexts to teach geometry.
Geometry in My World (MT)
- 1. Geometry in My World By Megan T 1
- 2. 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. 2
- 3. 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. 3
- 4. 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 4
- 5. 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. 5
- 6. 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 6
- 7. 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. 7
- 8. 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 8
- 9. 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 9
- 10. 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 10
- 11. 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°) 11
- 12. 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. 12
- 13. 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°. 13
- 14. 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. 14
- 15. 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. 15
- 16. 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. 16
- 17. 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. 17
- 18. 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. 18
- 19. 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. 19
- 20. 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. 20
- 21. 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 21