# Undefined terms in Geometry

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Undefined terms in Geometry
Please write the sponge in the space provided Sponge for Today: What is perspective?

Background Info The Renaissance was the beginning of a formal use of composition and perspective. The Renaissance ( ) was a great rebirth of European learning and discovery. It ended 1000 years of superstition and ignorance that followed the fall of Rome. The Renaissance began in Italy and spread throughout northern Europe. Renaissance artist include Michelangelo and Leonardo da Vinci, scientists like Galileo, and writers like Shakespeare.

Characteristics Renaissance artists…
investigating and representing the real world continued to depict religious subjects but also began to portray the human experience brought back the Greek classical ideals of ideal proportions (for depicting the human body as well as for architecture and painting)

Linear Perspective… Is based on the way human eye sees world-objects which are closer appear larger, and more distant objects appear smaller. Uses a vanishing point on the horizon line to create the illusion of space. Is created by drawing objects using orthogonal lines which lead to the vanishing point(s).

Linear Perspective Perspective is a technique for representing 3-dimensional space on a flat surface. During the Renaissance artists invented a mathematical system to show depth logically and consistently. System helped to create realistic art.

1 point vs. 2 point In one-point perspective, the forms are seen face on and are drawn to a single vanishing point. Objects seen at an angle would be drawn with two-point perspective using two vanishing points. Often these vanishing points are "off the page".

Other ways to Create Depth
The ways that artists make things look deep: Size: objects appear smaller as they get farther away. Position: objects appear higher on the page as they get farther away. Overlap: Overlapping objects show which is farther. Detail: Objects have less detail as they get farther away. Saturation of color: Close objects are brightest and sharpest. Objects in the distance appear pale and washed out. Atmospheric perspective: Objects in the distance may appear bluish. Warm colors advance/cool colors recede: Warm colors may appear closer. Cool colors may appear farther away.

Before the renaissance
How did artist create depth?

Is there Depth? 1 3 2 4 5 6 7

How to find Vanishing pt…
Identify the horizon on artwork.

How to find Vanishing pt…
Lines from objects to the horizon line create the vanishing point is clearly established. The lines leading to the vanishing point are called are called orthogonals.

1 pt perspective Look A cube in one-point perspective the front face of the form is seen as the closest point. The number of sides visible, whether or not you see the top or bottom of the box depends on the angle from which you view it.

Drawing a 1 pt Perspective object
Step 1 Orient your paper or draw a large rectangle on your board to represent a paper turned horizontally, or "landscape orientation."

Lines, lines, lines Every line you make in one-point perspective will be vertical, horizontal or an orthogonal line (irregular shapes and lines can be dealt with later). Make the end of the ruler flush with the edge of the paper. This is one of the most important and most challenging skills! If lines are not exactly horizontal and vertical, your students' drawings will be skewed!

Drawing a 1 pt Perspective object
Step 2 Draw a horizon line towards the top of the page and label it.

Drawing a 1 pt Perspective object
Step 3 Draw the vanishing point in the center of the horizon line and label it.

Drawing a 1 pt Perspective object
Step 4 Now draw a square or rectangle and label it "front face". Draw it in one of the lower corners so you have plenty of room to add more forms. You can continue to relate the drawing to the physical box model as you work.

Drawing a 1 pt Perspective object
Step 5 Now connect three corners of your rectangle or square to the vanishing point. These are orthogonals. Draw lightly so you can erase!

Drawing a 1 pt Perspective object
Step 6 Draw a horizontal line between the top two orthogonals where you want your form to end to make the top of the box.

Drawing a 1 pt Perspective object
Step 7 Draw a vertical line down from the horizontal line to complete the side.

Drawing a 1 pt Perspective object
Step 8 Erase the remaining orthogonals.

Drawing a 1 pt Perspective object
Step 10

Drawing a 1 pt Perspective object
Step 11

Drawing a 1 pt Perspective object
Step 12

Drawing a 2 pt Perspective object
Two-point perspective is useful to show an angle rather than face-on. Most lines are vertical or orthogonals drawn to two different vanishing points.

Class Work Draw a 2 point perspective drawing using the directions provided

Undefined terms in Geometry
Please write the sponge in the space provided Sponge for Today: What is perspective?

l Points, lines, Planes ● ● Locate & use symbolic language:
A point A line Collinear points Noncollinear points A line segment A ray Opposite rays A plane Intersection of 2 lines Intersection of 2 planes Undefined terms in Geometry Label your shape and draw arrows as follows… Q l P R E F Draw arrows at the ends of your horizon A D X G B C

Points, lines, Planes ● ● ● l Find point Q Find line l
You describe a point by writing the word point and using a capital letter: Point Q Find line l There are two different ways to describe a line: 1) naming any two points on the line with an line on top, or 2) writing line l Collinear points are points on the same line…such as point P, point Q, and point R (need three pts) Noncollinear points are points NOT on the same line…such as point D, point G, and point C (need three pts) P l Q Q R E F A D X G B C

Points, lines, Planes ● ● l P Q R E F A D ● X G B C
A line segment has two endpoints. You describe a line segment using two points with a segment on top A ray has one endpoint. You describe a ray by naming the initial point first and the directional point second with a ray on top Opposite rays look like a line A plane extends in four directions forever – it’s a surface You describe a plane by naming three noncollinear points or by one capital letter Intersection of 2 lines Intersection of 2 planes P l Q R E F A D X G B C