Career & Technical
n o i t a c u Ed
Basic Geometric Terms & Construction 004.00 Explain geometric terms and apply geometric construction techniques
Career & Technical
n o i t a c u Ed
Basic Geometric Terms & Construction 004.01 Explain selected geometric terms
Career & Technical
n o i t a c u Ed
Basic Geometric Terms & Construction 004.01 Explain selected geometric terms
Geometry
The study of the size and shape of things The relationship of straight and curved lines in drawing shapes It is essential to recognize geometry that exists within objects for the purpose of creating solid models or multiview drawings
Angles
Acute Angle
Measures more than 90
°
Right Angle
Vertex
°
Obtuse Angle
Measures less than 90
Measures exactly 90
°
Vertex
Point at which two lines of an angle intersect
Circle
Radius
Diameter
Distance across a circle through its center
Circumference
Distance from the center of a circle to its edge
Distance around the edge of a circle
Chord
Line across a circle that does not pass at
Circle
Has 360 Quadrant °
° 0 9
One fourth (quarter) of a circle Measures 90 °
Concentric
Two or more circles of different sizes that share the same center point
9 0 °
9 0 °
° 0 9
Triangles
Equilateral
Isosceles
All three sides are of equal length and all three angles are equal Two sides are of equal length
Scalene
Sides of three different lengths and angles with three different values
Triangles
Right Triangle
One of the angles equals 90
°
Hypotenuse
The side of a right triangle that is opposite the 90 angle °
HYPOTENUSE
Quadrilaterals
Square
Four equal sides and all angles equal 90 °
Rectangle
Two sides equal lengths and all angles equal 90 °
Trapezoid
Only two sides are equal length
Quadrilaterals
Rhombus
All sides are equal length and opposite angles are equal
Rhomboid
Opposite sides are equal length and opposite angles are equal
Regular Polygons
Pentagon
Hexagon
Five sided polygon
Six sided polygon
Octagon
Eight sided polygon
Regular Polygons
Distance across flats
Measurement across the parallel sides of a polygon
FLATS
Distance across corners
Measurement across adjacent corners of a polygon
CORNERS
Solids
Prism
Right Rectangular
Right Triangular
Solids
Cylinder
Cone
Sphere
Solids
Pyramid
Torus
Geometric Terms
Circumscribe
Process of creating a polygon that fully encloses a circle and is tangent to all of the polygons sides
Inscribe
Process of creating a polygon that is fully enclosed by a circle at its corners
Geometric Terms
Bisect
Divide into two equal parts
Tangent A line and arc, or two arcs that touch each other at one point only
Geometric Terms
Parallel
Two or more lines that are always the same distance apart
Perpendicular
Two lines that are at a 90 angle °
Geometric Symbols Angle Triangle R Radius Diameter
Parallel Perpendicular Square CL Centerline
Career & Technical
n o i t a c u Ed
Basic Geometric Terms & Construction 4.02 Demonstrate the procedures for drawing standard geometric constructions
Bisect a Line w/ a Compass
Given line AB
With points A & B as centers and any radius greater than ½ of AB, draw arcs to intersect, creating points C & D
Draw line EF through points C and D
Bisect a Line w/ a Triangle
H
Given line AB F
D
Draw line CD from endpoint A Draw line EF from endpoint B
E B
C A
Draw line GH through intersection
G
Bisect an Arc
Given arc AB
With points A & B as centers and any radius greater than ½ of AB, draw arcs to intersect, creating points C & D
Draw line EF through points C and D
Bisect an Angle
Given angle AOB
With point O as the center and any convenient radius R , draw an arc to intersect AO and OB to located points C and D
With C and D as centers and any radius R 2 greater than ½ the radius of arc CD, draw two arcs to intersect, locating point E
Draw a line through points and E to bisect angle AOB
O
Divide a Line into Equal Parts
Given line AB
Draw a line from endpoint A perpendicular to line AB
Position scale, placing zero on line AC at an angle so that the scale touches point B
Keeping zero on line AC, adjust the angle of the scale until any of the desired number of divisions are included between line AC and point B
Mark the divisions
Draw lines parallel to AC through the division marks to
A
C
B
Construct a Hexagon given distance Across Flats (Circumscribed)
Given distance across the flats of a hexagon, draw centerlines and a circle with a diameter equal to the distance across flats
With parallel edge and 30 – 60 ° triangle, draw the tangents °
Construct a Hexagon given distance Across Corners (Inscribed)
Given distance AB across the corners, draw a circle with AB as the diameter
With A and B as centers and the same radius, draw arcs to intersect the circle at points C, D, E, and F
Connect the points to complete the hexagon
C
D
A
B
F
E
Construct an Octagon Across Flats (Circumscribed)
Given the distance across the flats, draw centerlines and a circle with a diameter equal to the distance across flats With a parallel edge and 45 triangle, draw lines tangent to the circle in the order shown to complete the octagon
1 5
7
3
4
8
6 2
Construct an Octagon Across Corners (Inscribed)
Given the distance across the corners, draw centerlines AB and CD and a circle with a diameter equal to the distance across corners With the T-square and 45 triangle, draw diagonals EF and GH °
C G
E
B
A
H
F
Connect the points to complete the octagon
D
Construct an Arc Tangent to Two Lines at an Acute Angle A
Given lines AB and
Construct parallel lines at distance R
CD
Construct the perpendiculars to locate points of tangency
R
B O
C
R
D
With O as the point, construct the tangent arc using distance R
Construct an Arc Tangent to Two Lines at an Obtuse Angle A
Given lines AB and
Construct parallel lines at distance R
CD R O
Construct the perpendiculars to locate points of tangency With O as the point, construct the tangent arc using distance R
B
R
C D
Construct an Arc Tangent to Two Lines at Right Angles
Given angle ABC With B as the point, strike arc R 1 equal to given radius
A
R 2 D
With D and E as the points, strike arcs R 2 equal to given radius With O as the point, strike arc R equal to given radius
O
R
2
R 1
B
C E
Construct an Arc Tangent to a Line and an Arc
Given line AB and arc
Strike arcs
Draw construction arc parallel to given arc, with center O
Draw construction line parallel to given line AB
R 1
CD
(given radius)
From intersection E, draw EO to get tangent point T1, and drop perpendicular to given line to get point of tangency T2 Draw tangent arc R from T1 to T2 with center E O
C
R 1
E T1 R 1
A
B T2 D