# Geometry Fundamentals for Welding 171

The class "Geometry Fundamentals for Welding" teaches students how geometry is used in welding. A fundamental understanding of geometry and geometric concepts is a necessary skill for welding. This class discusses lines and angles, which are the basic building blocks of geometry. This class teaches users how to identify the parts of a circle and how to identify different types of triangles based on their sides and angles. In addition, this class includes lessons on how to find the area of a circle or triangle.

The relationship between lines and angles can be used to read and interpret welding blueprints, as well as machine settings. After this class, users will be able to understand and work with the basic building blocks of geometry. Users will also be able to calculate the area and circumference of a circle and the area of a triangle.

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## Class Details

Class Name:
Geometry Fundamentals for Welding 171
Version:
2.0
Difficulty:
Beginner
Number of Lessons:
19

## Class Outline

• Principles of Geometry in Welding
• Points, Lines, and Rays
• Parallel and Perpendicular Lines
• Parts of Angles
• Types of Angles
• Angle Basics Review
• Angle Pairs
• Transversals
• Circles and Semicircles
• Radius, Diameter, and Circumference
• Area of a Circle
• Tangents
• Review
• Triangles
• Types of Triangles: Angles
• Types of Triangles: Sides
• Interior Angles in a Triangle
• Calculating the Area of a Triangle
• Final Review

## Objectives

• Define geometry.
• Define points, lines, and rays.
• Describe perpendicular and parallel lines.
• Identify parts of angles.
• Describe types of angles.
• Describe angle pairs.
• Explain transversals.
• Describe circles. Describe semicircles.
• Describe the radius and diameter of circles. Calculate the circumference of a circle.
• Calculate the area of a circle.
• Describe tangents.
• Define triangle.
• Identify triangles using their interior angles.
• Identify different types of triangles using their sides.
• Describe the interior angles in a triangle. Calculate the unknown angle in a triangle.
• Calculate the area of a triangle.

## Glossary

Vocabulary Term Definition
acute angle An angle that measures less than 90 degrees. An acute angle is the smallest angle type.
acute triangle A triangle containing three angles that each measure less than 90 degrees. All three angles must add up to 180 degrees.
adjacent angles Two angles next to each other that share a common side and a common vertex. Adjacent angles form a larger single angle.
alternate angles Two angles that are located on opposite sides of the transversal line. Alternate angles will equal each other only if the lines intersected by the transversal are parallel.
alternate interior angles Angles that appear as two interior angles on opposite sides of an intersecting transversal. Alternate interior angles are created when a transversal crosses two parallel lines.
angle A geometric part feature created by two rays sharing an endpoint or the intersection of two straight lines. Angles are measured in degrees, which specify the amount of separation between the sides of the angle.
angles A geometric feature created by two rays sharing an endpoint or the intersection of two straight lines. Angles are measured in degrees, which specify the amount of separation between the two lines or rays.
area The size of the space contained within an enclosed two-dimensional figure. Area is typically measured in square units such as square inches or square centimeters.
base The side of a triangle that determines the height of the triangle. In an isosceles triangle, the base is the side that is not equal to the other sides.
base The side of the triangle that determines the height of the triangle. The base is the one side that is not equal to the other sides in an isosceles triangle.
base angles An angle that is formed by the base and one leg in an isosceles triangle. The base angles are always equal.
blueprints A document containing all the instructions necessary for making a project. A blueprint for welding includes points, lines, and angles.
butt joint A joint formed by two surfaces that meet without overlap or complex intersection. Butt joints attach two parts in the same plane.
circle A shape formed by a group of points that are an equal distance from a central point. The angles of a circle add up to 360 degrees.
circumference The boundary or perimeter around a circle. Circumference measures the distance around a circle.
complementary angles Two angles that measure exactly 90 degrees. Complementary angles can be adjacent or can be completely separate.
congruent Equal or similar to each other. All sides are congruent in an equilateral triangle, but none are congruent in a scalene triangle.
corner joint A type of joint made between two metal parts located at right angles to one another. A corner joint has a 90 degree angle.
corresponding angles Two angles that are located in matching corners of a transversal. Corresponding angles have the same measurement if a transversal crosses parallel lines.
cylindrical Having the shape of a circle. Cylindrical parts require welders to identify and calculate the dimensions of a circle.
diameter The distance from one edge of a circle to the opposite edge through the center. The diameter divides the circle in half.
equilateral triangle A triangle with three equal sides. Since all three sides of an equilateral triangle are the same length, all three angles must be equal.
exterior angles An angle located outside two lines in a transversal. Exterior angles can be equal to each other, depending on the relationship between the lines.
fillet weld A type of weld that is triangular in shape and joins two surfaces at right angles to one another. Fillet welds are the most common type of welds.
flare bevel A type of groove weld that is used to join a round or curved piece to a flat surface. Flare bevels are designed using circular geometry.
formulas A representation of a known equation using letters, symbols, or numbers. The formula 2 x π x r or π x d is used to calculate the circumference of a circle.
geometry The branch of mathematics that involves the measurements, properties, and relationships of shapes. Geometry involves the study of how lines and angles relate to physical shapes.
groove weld A type of weld that leaves an opening between two part surfaces, which provides space to contain weld metal. Groove welds are used on all joints except lap joints.
height A line drawn from the highest point in the triangle to the base. The height and base are always perpendicular.
infinite decimal number A decimal number that has no end and no repeating pattern. The most commonly known infinite decimal number is pi.
interior angles An angle located between two lines in a transversal. Interior angles can be equal to each other or can be supplementary.
intersect To meet, cut across, or overlap. Two intersecting lines form the shape of an "X."
intersect To meet, cut across, or overlap. Two lines that intersect form an "X."
isosceles triangle A triangle with at least two equal sides. An isosceles triangle also contains two equal interior angles.
joint The meeting point of the two materials that are fused together. Welding creates a permanent joint.
joint design The specification of a particular welded joint and its required dimensions. Joint design requires measuring angles and dimensions.
lap joint A joint formed by two overlapping pieces of metal. Lap joints form parallel lines.
legs The two equal sides in an isosceles triangle. Since the legs of an isosceles triangle are equal in length, the opposite angle must be equal.
line segment A section of a line with two endpoints that indicate where the section ends. A line segment is perfectly straight and one dimensional.
lines A series of points that extends endlessly in two directions. A line is perfectly straight, and its length cannot be measured.
mathematics The study of numbers and quantities and their relationships. Mathematics includes the logic and rules used to solve numerical problems.
obtuse angle An angle that measures greater than 90 degrees but less than 180 degrees. A welded Y-joint features an obtuse angle.
obtuse triangle A triangle containing one angle that is greater than 90 degrees. The other two angles most total less than 90 degrees when added together.
one-dimensional An object that has only height, width, or length. A geometric line is one-dimensional because only its length can be measured.
parallel lines Two lines in the same plane that, no matter how far they extend, do not intersect with each other. Parallel lines are the same distance apart at any given point.
perpendicular Two lines that intersect to form a 90° angle. The measurement of the right angle formed by perpendicular lines may be indicated with a square instead of a number of degrees.
pi An infinite decimal number used to calculate the circumference and area of a circle. Pi is often simplified to the decimal 3.14.
plane A flat surface that extends infinitely in any direction in two dimensions. The two parts of a butt weld are used to join components lying in one plane.
point A definite location or position that has no width, depth, or length. A point is usually represented on blueprints by a dot.
point of tangency The point at which a tangent touches the circumference of the circle, also known as a tangent point. A radius drawn to the point of tangency is always perpendicular to the tangent line.
points A dot that indicates a definite location or position. A point has no width, depth, or length.
radius The distance from the center to the edge of a circle. All radii of a circle are equal in length.
ray A portion of a line that has only one endpoint and extends infinitely in one direction. A ray's length cannot be measured.
rays A portion of a line that has only one endpoint and extends infinitely in one direction. A ray's length cannot be measured.
reflex angle An angle that measures more than 180 degrees but less than 360 degrees. Reflex angles may help determine the values of unknown angles.
right angle An angle that measures exactly 90 degrees. Right angles are formed by two lines that are perpendicular to one another.
right triangle A triangle containing exactly one 90° angle. The other two angles must total exactly 90 degrees.
scalene triangle A triangle with three unequal sides. The angle opposite the longest side is the largest angle.
semicircle A half circle. The angles of a semicircle add up to 180 degrees.
square The product of multiplying a number by itself. Squaring is notated by a superscript 2 next to the number.
square inches A unit of area measurement that is equal to a square with sides that are one inch long. Square inches are found by multiplying the square's length and height, which is the same as squaring 1 inch (1²).
straight angle An angle that measures exactly 180 degrees. Straight angles may appear as a line, line segment, or ray.
sum The resulting amount from combining or adding numbers together. The sum of the measurement of interior angles of triangles is always 180 degrees.
supplementary angles Two angles that measure exactly 180 degrees. Supplementary angles are always adjacent angles.
supplementary interior angles Two angles whose measurements equal 180 degrees. Supplementary interior angles appear as two interior angles on the same side of the transversal.
tangent A line, line segment, or ray that touches a circle at exactly one point on the circle's circumference. Tangents often appear in blueprints when a cylindrical object touches a flat surface.
tangent point The point at which a tangent touches the circle on its circumference, also known as a point of tangency. A radius drawn to the tangent point is always perpendicular to the tangent line.
T-joint A type of joint formed between two perpendicular metal parts, forming the shape of the letter &#34;T.&#34; T-joints also contain right angles and perpendicular lines.
transversal A line that intersects two or more lines at different points. A transversal forms several different angles with the lines that it intersects.
triangle A closed figure with exactly three sides. The three sides meet to form three interior angles.
two-dimensional Having length and width but no depth. A plane can be measured in two dimensions because it has both length and width, but no depth.
vertex The point of an angle where its two sides meet. On some prints, an angle may be identified only by its vertex.
vertex angle The angle formed by the two equal legs in an isosceles triangle. The vertex angle is always opposite the base.
vertical angles Two angles opposite each other that share the same vertex and are formed by intersecting lines. Vertical angle pairs always have the same measurement in degrees.
volume The amount of filler metal deposited in a weld. The volume of a weld involves calculating the area of a welded joint.
Y-joint A type of joint used in pipe welding. Y-joints have an obtuse angle and an acute angle.