Download Geometry Journal 4

Geometry Journal 4
Michelle Habie 9-3
Triangles:
Sides:
Scalene (3 sides are different)
Equilateral (3 sides are thesame)
Issoceles (2 sides are equaland 1 isdifferent)
Angles:
Acute (3 anglesmeasurelessthan 90°)
Right (1 anglemeasures 90°)
Obtuse(1 anglesmeasuresgreaterthan 90°)
We use each
type of triangle
according to its
sides and its
angle
measurement
because each
of them, has
different
properties and
uses.
Examples:
IssocelesTriangle
Right Triangle
to measure
the shape of
the building.
Obtuse–
roofof a
house.
Equilateral- to build
games made of iron.
Scalene
Partsof a Triangle:
1 angle
Parts:
3 sides
3 interior angles
1 exterior angle for each side
Hypotenuse
Hyoptenuse
1 side
1 side
1 angle
1 angle
1 side
The exterior angle is formed by the extension of one side of the
triangle. The exterior angle has two remote interior angles
which are non-adjacent to the exterior one.
An interior angle is formed when two sides of a triangle meet.
Triangle Sum Theorem:
It states that the sum of the 3 interior angles of any triangle have
to be equal to 180 degrees.
Ang. A+ Ang. B+ aNG. C =180
X+19+2x+1+100=180
3x+120=180
3x=60
X=20
Examples:
Interior:
3x+5
B
A
118
5x+1
2x+3
B
X+19
3x+5+2x+13=118
5x+18=118
5x=100
X=20
99
X+8
A
100
2x+1
5x++x+8=99
6x+9=99
6x=90
x=15
Exterior:
3x-10
2z+1
2
25
X+15
10
6z-9
4
1
3
C
Exterior AngleTheorem:
States that the exterior angle is the same as the sum of the
two remote interior angles.
How can it be used?
It can be used in navigation to find angles by knowing two
and find the target or the place they are leading to.
Congruence:
Congruenceforshapesmeansthattheobjectshavethes
ameshapeandthesamemeasurementswhilecorresp
onding in
shapesmeanssidesthatocupythesameposition.
Whileprovingtwotriangles are congruentyou may
needgoprovethecorrespondingsidesorangles are
congruentandthenjumpinto a
conclusionthatthetwotriangles are congurent by
the CPCTC.
MeaningthattheCongruentPartsoftheCongruentTrian
gles are alwayscongruent.
CPCT Examples:
4cm
10cm
8cm
8cm 8cm
8cm
8cm
4cm
8cm
13 cm
10cm
6cm
13cm
15 cm
15 cm
13cm
6cm
13 cm
SSS Postulate:
If three sides of one triangle are congruent
to three sides of another triangle, the the
triangles are congruent.
Examples:
16cm
9cm
9cm
5cm
9cm
9cm
16cm
5cm
24 cm
16cm
16cm
SAS Postulate:
This type of postulate is used to prove that
two triangles are congruent. This postulate
says that if two sides of one triangle and
the included angle of it, and congruent=not
to the corresponding two sides and the
included angle of the second triangles,
than the two figures are congruent.
Examples:
1.
V
C
E
D
Y
F
A
X
Z
B
ABC congruent
1
EFD
4
2
6
3
U
5
123 congruent
456
XYZ congruent
W
UVW
ASA Postulate:
If two angles and the included side of one
triangle are congruent to two angles and
the included side of another triangle, then
the traingles are congruent.
Examples:
25
25
32
32
25
76
100
100
25
90
90
76
30
27
15
30
15
27
AAS Theorem:
If twoangles and a non included side of one
triangle are congruent to the
corresponding angles and non included
side of another triangle, then the triangles
are congruent.
Examples:
= angle
30
30
75
75
8in
14
21
9 cm
9 cm
21
14
8in