Download vertex (end) rays (sides) 180

Unit 19 Introduction to Geometry
Read through Unit 19. This unit is mainly vocabulary and formalizing some of the intuitively obvious
‘postulates and axioms from geometry
Some vocabulary and symbolism from Unit 19 to know:
Point, line symbolized by a dot and named with a capital letter
A line refers to a never ending straight line it is named by two points like this
A curved line has no straight parts
AB
A line segment is part of a line that has end points It is named by the end points like this
AB
Parallel lines never cross (intersect). AB  CD lines AB and CD are parallel
Perpendicular lines cross at 90° or right angles symbolized with ⊥
Oblique lines are neither parallel nor perpendicular
Unit 20 Angle Measure
Angles are measured in degrees or radians.
The interior angle is inside the rays
The exterior angle is the long way around
Angles are named by three points in order or just the
vertex ∠ABC or ∠B
A
rays (sides)
B
C
Positive rotation is in a counter clockwise direction.(The
right hand rule for upward motion is positive)
vertex (end)
One complete rotation is 360°° or 2π
π radians
1/2 of a complete rotation
=
Degrees
Radians
1/4 of a complete rotation
=
1 radian =
180 π
Degrees
Radians
When working with angles expressed in degrees, the partial degrees may be expressed as decimal or as
minutes and seconds
To convert between degrees, minutes, seconds and decimal degrees remember
60 seconds = 1 minute and 60 minutes = 1 degree.
Rounding rules: two decimal places for minutes another two for seconds
1.
Convert 25°26’ 38”to decimal
2.
Convert 36.12° to degrees minutes
Add or subtract these angles. Notice that adding degrees with minutes and seconds is a lot like adding
inches, feet and yards. Be sure to borrow and bump up correctly
3.
27 44'
+ 6216'
5016'
4.
5.
− 45 48'
1514'25"
− 23 07'12"
When multiplying or dividing distribute, and then bump up or down as necessary and round off
6. 5 x (18° 22’)
7. (192°55’04”) ÷ 8
More Angle Vocabulary Unit 21
Adjacent angles have a common vertex and a
common side
A transversal is a line that intersects two or more
lines
Opposite angles of intersecting lines have equal
measures.
When a transversal crosses two or more parallel
lines, alternate angles have equal measures and
corresponding angles have equal measures
Determine the Angle measures
8.
9.
B
A
A
38°
D
25°
C
D
B
E
C
F
Triangles Unit 22
Some vocabulary to use when working with triangles comes from the classifying triangles either by the
number of equal sides or by the measures of the angles
Equilateral triangle
has equal sides
and equal angles
of 60° each
A Isosceles triangle
has two equal sides
The angles opposite these have
the same measure.
leg
A Right triangle
has one 90° angle
leg
leg
hypotenuse
leg
base
The 30° – 60° – 90° triangle
The Isosceles Right triangle
has a 90° angle and two equal
angles and two equal sides
This one is actually an equilateral
triangle cut in half, The longest
side is twice as long as the
shortest side
The 3 – 4 – 5 triangle
(Also a right triangle)
The numbers describes the
proportion of the sides
Some other very important triangle relationship
The sum angles in every triangle add up to 180°
1.
A triangle has angles of 124° 57’ and 27° 54’. What is the measure of the third angle?
A line that bisects an angle in a triangle, bisects the opposite side
In an isosceles or equilateral triangle, the bisecting line is
perpendicular to the base.
2.
In the Isosceles triangle shown Find the measure of
angle A and the length of BD if ∠ACB = 36° and
side AB is 20.0 cm long
C
A
B
D
Pythagorean Theorem
The Pythagorean Theorem or a2 + b2 = c2 relates the sides of a right triangle
In a right triangle, the side opposite the right angle is called the hypotenuse The other two sides
are the legs
The hypotenuse is always designated as side c
Show that this relationship holds true for these 3 – 4 – 5 triangle.
4.
3.
5.0cm
15.0cm
3.0cm
9.0cm
4.0cm
12.0cm
Find the missing side(s) of these triangles.
5.
6.
An Isosceles Triangle
x
6.0 m
3.0 cm
10.2 cm
x
9.8 m
Congruent and Similar Figures Unit 23
Congruent figures are of exactly the same size and shape
Similar figures have the same shape but not the same size. Corresponding sides of similar figures are
directly proportional, corresponding angles are equal.
1.
The figures are similar. Determine the dimensions of the larger figure.
H
8.0 in
D
12.3 in
G΄
C
5.0 in
6.5 in
A
6.0 in
B
E
F
Polygons are similar if all of the following are true:
All the corresponding sides are proportional and
All the angles are equal.
2.
3.
Determine the length of vertical braces A and B that are
placed in a truss with outside measurements of 16.0ft 12.0ft
and 20.0ft, if brace A is 5.0ft from the center support and
brace B is 3.0 ft from the center support. The top angle of this
truss is 90° and the braces are perpendicular to the bottom of
the truss.
A
B
The side view of a uniformly tapered shaft is shown. Compute the shaft diameter 70.0mm from end, if
the shaft tapers from a diameter of 14.5mm to 32.0 mm over a distance of 120.0mm