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68 Cards in this Set
- Front
- Back
What is the name given to the simplest polygon? |
Triangle |
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True or False? |
False, |
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How do you find the number of diagonals ? |
n(n-3) 2 |
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How do you find the sum of the angles in a geometric figure? |
n(n-2)x180 |
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What is the name given to the pieces of a tangram? How many pieces are there? What geometric shapes are in these pieces? |
7 pieces in a tangram each piece is called a tan the shapes are triangles, square, and parallelogram |
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What makes a polygon regular? How many regular polygons are there? What are they? |
All sides are the same measure there are 3 regular polygons: equilateral triangle, square, and regular hexagon |
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What is unique about polyhedra? What is another name for polyhedra? How many are there? |
all faces & sides are the same measure (identical) Platonic Solids |
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What are the major parts of a polyhedron(platonic solids) |
faces edges vertices |
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What is the fewest # of vertices that a polyhedron can have? Why? |
4 |
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What is Euler's formula? (Finding # of faces, vertices, or edges) |
F+V-E=2 |
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What are the geometric terms that can be used when discussing a square? |
rhombus rectangle rest of 4 sided figures |
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What are the names for triangles when discussing their angles measures? Why do they have these names? |
Acute: all angles are less than 90 degrees Obtuse: one angle is greater than 90 but less than 180 Right: one angles measures 90 |
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What are the names of triangles when discussing the lengths of their sides? Why do they have these names? |
Scalene: all sides have a different measure Equilateral: all sides have the same measure Isosceles: two sides of the triangle are the same measure, the other one is different. |
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What is the major difference in a polygon & a polyhedron? |
polygon: 2D figure with sides polyhedron: 3D figure with faces and edges |
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What are the names given to the two most important types of polyhedron? |
Pyramids & Prisms |
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What happens each time another side is added to a polygon? |
The name changes |
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Where do we find numerous examples of line symmetry? Give an example. |
In nature, an example is a butterfly |
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What does the "order of rotation symmetry" mean? |
how many times a shape rotates before getting back to its original shape. |
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What does a line of symmetry enable us to conclude about angles of triangles? |
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Give a general definition of symmetry of a figure |
the movement of a shape to the points until it gets back to the original shape |
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Is there rotational symmetry of order 1? |
No, this is called trivial symmetry |
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List the 3 types of symmetry & its informal name? |
Reflection-mirror line Rotation-turn Point-origin |
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What is the difference in a regular tessellation and a semi-regular tessellation? |
Regular: made up of regular polygons Semi-regular: made up of 2 or more regular polygons |
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What is a tessellation? |
a repeating pattern that covers a plane without overlapping and leaving no gaps |
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What 2 figures always tessellate in the plane? |
all quadrilaterals triangle |
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What mathematician gave us the tessellation? |
M.C. Escher |
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How many regular polygons tessellate? |
3 squares regular hexagons |
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True or False? "We get rotational symmetry for a circle by rotating it about the center of the circle. So a circle has exactly 360 rotational symmetries." |
False, there are infinitely many |
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Identify the 2 letters of the alphabet that have no countable symmetries. |
J & K |
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Is it true that "If a figure is turned about a point, its reflection is obtained."? Why or why not? |
False, you will get rotation |
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How many regular tessellations are there? How many semi-regular? |
3 regular 8 semi-regular |
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How does one name a tessellation? |
by the # of sides of the shapes. 1. pick a vertex 2. any shape touching that point you include in the name |
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True or False? If an equilateral triangle is rotated counterclockwise; there will be new rotational symmetries in addition to those if the equilateral triangle is rotated clockwise. |
False, it's an equilateral triangle, they would have the same amount. |
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Why do we say that all figures have a 360 degree rotation, but some have more? |
Some shapes have more rotations than 1, so a square for example has an order of 4 |
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Give 2 examples of similar figures? |
straight lines circles |
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What is the difference between similarity & congruency? |
similarity: same shape with different sizes congruency: same shape and size |
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What three criteria hold if 2 triangles are similar? |
AAA/AA SSS |
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Give 2 forumlas for the scale factor |
new length _____________ = scale factor old length scale factor x old length = new length |
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what is the definition for dilation? |
type of transformation that produces the same shape as the original by enlarging or reducing the size around a certain point. |
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Suppose the scale factor for the dilation of a figure is 1, what will be true of the image? |
the size of the pre image & image will be the same size. |
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What symbol is used to show that 2 figures are similar? |
tilde ~ |
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What is another name for scale factor? |
similarity ratio |
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2 shapes are similar if.... |
1. corresponding angles are equal 2. corresponding sides are proportional by the scale factor |
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What is the difference between central and inscribed angles? |
Central: vertex is the center of the circle Inscribed: vertex on the edge of the circle made up of chords, & intercepts an arc. |
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What are the 2 main "pieces" of a circle? |
segment: made from a chord sector: a pizza slice |
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What is the name given to circles that share the same center? |
concentric circles |
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What is unique about a tangent line? |
on the outside of the circle & touches @ only 1 point as it passes by. |
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what is another name for the original figure? |
pre-image |
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How do you obtain pi? |
circumference _______________ diameter |
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what must be true of the circle if the circumference is pi? |
Diameter is 1 |
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what is "a part" of the circumference called? |
arc 1. major 2. minor |
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What is the mnemonic device for the basic metric prefixes |
King Henry Died Drinking Chocolate Milk |
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What is the driving force for everyone to use the metric system? |
International Trade |
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Are measurements exact? Why or why not. What unit gives a better approximation? |
No, use the smallest unit possible for less room for error. |
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An isometry is..... |
a rigid motion |
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Name the 4 transformations |
reflection rotation translation glide reflection |
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what are the 4 body parts used for measurement? Which one is used today? |
hand - still used today span cubic foot |
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what are the informal terms for the transformations? |
translation: slide rotation: turn reflection: flip |
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Is a dilation a transformation? Is it an isometry? |
Yes, a dilation is a transformation. |
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Is every characteristic easy to quantify? Name at least one that is not. |
No, for example, emotions |
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How would you explain how one can determine the measure of an exterior angle of a triangle if they are given the measures of the interior angles? |
add the measures of the interior angles (opposite of the exterior angle) |
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What are 2 names that apply to our measurement system? |
english british customary traditional |
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In a transformation what is true of the original and it's image? |
They NEVER change shape or size
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what is the official name for the metric system? |
international system of unit |
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what are pythagorean triples? |
positive integers that fit the pythagorean theorem |
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what is Pythagoreas' version of the Pythagorean Theorem |
area of region 1 + area of region 2 = area of region 3 |
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What is the Pythagorean Theorem in words? |
the square of the hypotenuse is the sum of the other 2 legs |
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Since Pythagreas' time, how many justifications for this theorem have there been? Name 3 famous people who provided a justification. |
More than 350 Euclid, Leonardo De Vinci, President James Garfield |