GEOMETRY OF 2D SHAPES
TRIANGLES
h triangie Sa closed figure with three sides.Triangles can be classified intwo ways:
1) According to the size of their
angles.
Acute-angled Atriangle where all three angles are
triangle acute angles (greater than 0° but less
than 90°).
Obtuse-angled Atriangle where one angle is obtuse
triangle angled (greater than 90° but less than
180°). The other two angles are acute
angles. Obtuse angle
Right-angled A triangle where one angle is equal to
triangle 90°.The other two angles are acute
angles and sum to 90°. The side
opposite the 90° angle is called the
hypotenuse. Hypotenuse
2) According to the length of their sides.
Equilateral A
triangle where: A AB = BC = AC
Triangle
(equilateral A) all three sides are the
and
same length.
All three angles are 60°.
B Â = B= = 60°
Isosceles Atriangle where:
AB = BC
Triangle
two sides are the same
(isos. A) and
length.
The two angles opposite B
the sides of equal length
are equal.
Atriangle where all sides are A
Scalene different lengths and all three
Triangle
angles are different sizes. AB # BC # AC
B
The largest angle will be C
opposite the largest side. The
smallest angle will be opposite
the smallest side.
94 | Page
, PROPERTIES OF TRIANGLES
Interior angles The interior angles of a
of a triangle. triangle add up to 180°.
A
(<'s of a A) Â+Ê+ = 180°
B
Exterior angle The angle formed by
B
Exterior angle BD = Â + Ê
of a triangle extendingany one of
(ext. < of a the three sides of a
triangle is called the D
exterior angle of the
triangle.
The exterior angle of a
triangle equals the sum
of the interior opposite
angles.
NAMING TRIANGLES
triangle belowis named
The
alphabetical order according the vertices.
We usually name triangles in
AFGH.
Examples diagrams:
variables in each of the following
Determine the values of the
REASON
STATEMENT
(1)
A B
a/A C
d/S7° 128° G C i80-128°
D E
latbic: IsO° Ls on a stc lne
T'b462°: 180°
b=l80 (04
b 7i
, STATEMENT REASON
(2)
Lepp- sices
2y - 20
43° Ry-leo
2
(3) STATEMENT REASON
(a) Solve for x giving reasons
(b) Classify AXYZ, with reasons.
W
*+ 50°
ZAS0-180°
8O0°-180°
-30° I3o.18O° -450
Y
AxYZisOsceles
Geometry
keeps you
in shape.
TRIANGLES
h triangie Sa closed figure with three sides.Triangles can be classified intwo ways:
1) According to the size of their
angles.
Acute-angled Atriangle where all three angles are
triangle acute angles (greater than 0° but less
than 90°).
Obtuse-angled Atriangle where one angle is obtuse
triangle angled (greater than 90° but less than
180°). The other two angles are acute
angles. Obtuse angle
Right-angled A triangle where one angle is equal to
triangle 90°.The other two angles are acute
angles and sum to 90°. The side
opposite the 90° angle is called the
hypotenuse. Hypotenuse
2) According to the length of their sides.
Equilateral A
triangle where: A AB = BC = AC
Triangle
(equilateral A) all three sides are the
and
same length.
All three angles are 60°.
B Â = B= = 60°
Isosceles Atriangle where:
AB = BC
Triangle
two sides are the same
(isos. A) and
length.
The two angles opposite B
the sides of equal length
are equal.
Atriangle where all sides are A
Scalene different lengths and all three
Triangle
angles are different sizes. AB # BC # AC
B
The largest angle will be C
opposite the largest side. The
smallest angle will be opposite
the smallest side.
94 | Page
, PROPERTIES OF TRIANGLES
Interior angles The interior angles of a
of a triangle. triangle add up to 180°.
A
(<'s of a A) Â+Ê+ = 180°
B
Exterior angle The angle formed by
B
Exterior angle BD = Â + Ê
of a triangle extendingany one of
(ext. < of a the three sides of a
triangle is called the D
exterior angle of the
triangle.
The exterior angle of a
triangle equals the sum
of the interior opposite
angles.
NAMING TRIANGLES
triangle belowis named
The
alphabetical order according the vertices.
We usually name triangles in
AFGH.
Examples diagrams:
variables in each of the following
Determine the values of the
REASON
STATEMENT
(1)
A B
a/A C
d/S7° 128° G C i80-128°
D E
latbic: IsO° Ls on a stc lne
T'b462°: 180°
b=l80 (04
b 7i
, STATEMENT REASON
(2)
Lepp- sices
2y - 20
43° Ry-leo
2
(3) STATEMENT REASON
(a) Solve for x giving reasons
(b) Classify AXYZ, with reasons.
W
*+ 50°
ZAS0-180°
8O0°-180°
-30° I3o.18O° -450
Y
AxYZisOsceles
Geometry
keeps you
in shape.
