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68 Cards in this Set

  • Front
  • Back

What is the name given to the simplest polygon?

Triangle

True or False?
The two acute angles in a right triangle are supplementary.

False,

How do you find the number of diagonals ?

n(n-3)
________


2

How do you find the sum of the angles in a geometric figure?

n(n-2)x180

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

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

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
There are 5 different platonic solids(Polyhedra)

What are the major parts of a polyhedron(platonic solids)

faces


edges


vertices

What is the fewest # of vertices that a polyhedron can have? Why?

4

What is Euler's formula? (Finding # of faces, vertices, or edges)

F+V-E=2

What are the geometric terms that can be used when discussing a square?

rhombus


rectangle


rest of 4 sided figures



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

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.

What is the major difference in a polygon & a polyhedron?

polygon: 2D figure with sides


polyhedron: 3D figure with faces and edges

What are the names given to the two most important types of polyhedron?

Pyramids & Prisms



What happens each time another side is added to a polygon?

The name changes

Where do we find numerous examples of line symmetry? Give an example.

In nature, an example is a butterfly

What does the "order of rotation symmetry" mean?

how many times a shape rotates before getting back to its original shape.

What does a line of symmetry enable us to conclude about angles of triangles?

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

Is there rotational symmetry of order 1?

No, this is called trivial symmetry

List the 3 types of symmetry & its informal name?

Reflection-mirror line


Rotation-turn


Point-origin

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

What is a tessellation?

a repeating pattern that covers a plane without overlapping and leaving no gaps

What 2 figures always tessellate in the plane?

all quadrilaterals


triangle

What mathematician gave us the tessellation?

M.C. Escher

How many regular polygons tessellate?

3
equilateral/equiangular triangles


squares


regular hexagons

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

Identify the 2 letters of the alphabet that have no countable symmetries.

J & K

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

How many regular tessellations are there? How many semi-regular?

3 regular


8 semi-regular

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

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.

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

Give 2 examples of similar figures?

straight lines


circles



What is the difference between similarity & congruency?

similarity: same shape with different sizes


congruency: same shape and size

What three criteria hold if 2 triangles are similar?

AAA/AA


SSS
SAS

Give 2 forumlas for the scale factor

new length


_____________ = scale factor


old length




scale factor x old length = new length

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.

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.

What symbol is used to show that 2 figures are similar?

tilde ~

What is another name for scale factor?

similarity ratio

2 shapes are similar if....

1. corresponding angles are equal


2. corresponding sides are proportional by the scale factor

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.

What are the 2 main "pieces" of a circle?

segment: made from a chord


sector: a pizza slice

What is the name given to circles that share the same center?

concentric circles

What is unique about a tangent line?

on the outside of the circle & touches @ only 1 point as it passes by.

what is another name for the original figure?

pre-image

How do you obtain pi?

circumference


_______________


diameter

what must be true of the circle if the circumference is pi?

Diameter is 1

what is "a part" of the circumference called?

arc


1. major


2. minor

What is the mnemonic device for the basic metric prefixes



King Henry Died Drinking Chocolate Milk

What is the driving force for everyone to use the metric system?

International Trade

Are measurements exact? Why or why not. What unit gives a better approximation?

No, use the smallest unit possible for less room for error.

An isometry is.....

a rigid motion

Name the 4 transformations

reflection


rotation


translation


glide reflection

what are the 4 body parts used for measurement? Which one is used today?

hand - still used today


span


cubic


foot

what are the informal terms for the transformations?

translation: slide


rotation: turn


reflection: flip

Is a dilation a transformation? Is it an isometry?

Yes, a dilation is a transformation.
But, in a dilation the size of the shape changes so therefor cannot be an isometry.

Is every characteristic easy to quantify? Name at least one that is not.

No, for example, emotions

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)

What are 2 names that apply to our measurement system?

english


british


customary


traditional

In a transformation what is true of the original and it's image?

They NEVER change shape or size

what is the official name for the metric system?

international system of unit

what are pythagorean triples?

positive integers that fit the pythagorean theorem

what is Pythagoreas' version of the Pythagorean Theorem

area of region 1 + area of region 2 = area of region 3

What is the Pythagorean Theorem in words?

the square of the hypotenuse is the sum of the other 2 legs

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