Transcript Aim: Do Now: 1) If

Aim: What are polygons? How do we classify triangles?
Do Now:
1) If APD is a straight angle, mAPB  2 x  2 ,
mBPC  10 x , mCPD  8 x  2 , determine:
C
a) x
B
b) mAPB, mBPC , mCPD
A
D
P
c) Classify the type of each angle:
APB, BPC , CPD , APC
2) Which of the following shapes are polygons?
a)
d)
c)
b)
e)
f)
Geometry Lesson: Polygons,
Triangles
1
Def: Polygons A polygon is a closed figure that is the
union of line segments that intersect only
at their endpoints.
Def: Regular All angles and all sides of a regular
Polygons:
polygon are equal in measure.
Geometry Lesson: Polygons,
Triangles
2
Triangles: A triangle is a polygon with exactly three
sides.
P
Q
Sides of PQR
PQ or QP
QR or RQ
RP or PR
PQR
R
Angles of PQR
PQR or RQP or Q
QRP or PRQ or R
RPQ or QPR or P
Geometry Lesson: Polygons,
Triangles
3
“Included” Sides and Angles of Triangles
P
PQR
R
Q
Two angles that share a side “include” the side.
1) PQ is included by angles P and
and Q .
2) Angles Q and
and R include side QR .
3) Side RP is included by R and P.
Two sides “include” the angle between them.
1) P is included by sides QP and
and PR .
2) Angle Q is included by sides QP and QR
3) Sides QR and
and PR include R .
Geometry Lesson: Polygons,
Triangles
4
“Opposite” Sides and Angles of Triangles
P
Q
PQR
R
Each angle of a triangle has an opposite side, and vice versa.
1) P is opposite side QR .
2) Angle R is opposite side QP .
3) Side PR is opposite Q .
Geometry Lesson: Polygons,
Triangles
5
Classifying Triangles by Sides:
Def: An Equilateral triangle
has three congruent sides.
Def: An Isosceles triangle has
at least two congruent sides.
Def: A Scalene triangle
has no congruent sides.
Geometry Lesson: Polygons,
Triangles
6
Isosceles Triangle:
1) The 2 congruent sides are known as Legs..
2) The non-congruent side is the Base.
.
3) Angles opposite the legs are the Base Angles.
.
4) The angle included by the legs is the Vertex Angle.
.
B
P vertex
What type of triangle is CED ?
Base
PQ
C Base
A
CE
Legs
PR, QR
Q
Legs
leg
leg
CD
Vertex Angle ED, 
R
Angle
E
D R Vertex
D
Base Angles
P, Q
ABCDE is a
Angles
angleCED, DCE
base angleregular pentagon Basebase
B
A base
C
Geometry Lesson: Polygons,
Triangles
7
Classifying Triangles According to Angles:
Def: A triangle having three acute angles
is an Acute Triangle.
triangle.
Def: A triangle having three congruent
angles is an Equiangular Triangle.
triangle.
Def: A triangle having a right
angle is a Right Triangle.
triangle
Def: A triangle having an obtuse
angle is an Obtuse triangle
Triangle.
Geometry Lesson: Polygons,
Triangles
8
Right Triangles:
1) The side opposite the right angle is the Hypotenuse. .
2) The sides opposite the acute angles are Legs..
3) The longest side is the Hypotenuse..
4) Pythagorean Theorem: a 2  b 2  c 2
5) If a 2  b2  c 2 , then the triangle is a right triangle
Example: A triangle has sides measuring 9, 12,
hypotenuse
and 14 cm. Show
that
this
triangle
is
not
a
right
c
leg
a
triangle.
a 2  b2  c 2
9  12  14 leg
b
81  144  196
225  196
Geometry Lesson: Polygons,
2
2
2
Triangles
9