Download Informal Geometry

Geometry Agenda

Warm up

Mapquest 2

Interior/Exterior Triangle Angles


Notes
Practice
Session 5
Begin at the word “Today”.
Every Time you move, write
down the word(s) upon which
you land.
Warm-up
is
Show
Spirit!
1. Move to the corresponding angle.
homecoming!
2. Move to the vertical angle.
Today
3. Move to the supplementary angle.
4. Move to the alternate interior angle.
5. Move to the vertical angle
school
your
.
6. Move to the alternate exterior angle.
GO
7. Move to the consecutive exterior angle.
JAGS!
MAPQUEST 2
CCGPS Analytic Geometry
UNIT QUESTION: How do I prove
geometric theorems involving lines,
angles, triangles and parallelograms?
Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13
Today’s Question:
If the legs of an isosceles triangle are
congruent, what do we know about
the angles opposite them?
Standard: MCC9-12.G.CO.10
Triangles & Angles
September 27, 2013
Base Angles Theorem
If two sides of a triangle are congruent, then the
angles opposite them are congruent.
If AB  AC , then B  C
Converse of Base Angles
Theorem
If two angles of a triangle are congruent, then
the sides opposite them are congruent.
If B  C , then AB  AC
EXAMPLE 1
Apply the Base Angles Theorem
Find the measures of the angles.
SOLUTION
Q
P
Since a triangle has 180°, 180 – 30 =
150° for the other two angles.
Since the opposite sides are congruent,
angles Q and P must be congruent.
150/2 = 75° each.
(30)°
R
EXAMPLE 2
Apply the Base Angles Theorem
Find the measures of the angles.
Q
P
(48)°
R
EXAMPLE 3
Apply the Base Angles Theorem
Find the measures of the angles.
Q
(62)°
R
P
EXAMPLE 4
Apply the Base Angles Theorem
Find the value of x. Then find the measure of each angle.
P
Q
(20x-4)°
SOLUTION
R
Since there are two congruent
sides, the angles opposite them
must be congruent also. Therefore,
12x + 20 = 20x – 4
20 = 8x – 4
Plugging back in,
mP  12(3)  20  56
mR  20(3)  4  56
24 = 8x
3=x
And since there must be 180
mQ  180  56  56  68
degrees in the triangle,
HYPOTENUSE
LEG
LEG
Interior Angles
Exterior Angles
Triangle Sum Theorem
The measures of the three interior angles
in a triangle add up to be 180º.
x°
y°
x + y + z = 180°
z°
Find mT in RST.
R
m R + m S + m T = 180º
54º + 67º + m T = 180º
121º + m T = 180º
54°
S
67°
T
m T = 59º
Find the value of each variable in DCE
E
B
y°
C
x°
85°
55°
A
m  D + m DCE + m E = 180º
55º + 85º + y = 180º
140º + y = 180º
y = 40º
D
Find the value of each variable.
x°
43°
x°
x = 50º
57°
Find the value of each variable.
55°43°
28°
x = 22º
y = 57º
Find the value of each variable.
50°
53°
62°
x = 103º
x°
50°
Exterior Angle Theorem
The measure of
the exterior
angle is equal to
the sum of two
nonadjacent
interior angles
1
m1+m2 =m3
2
3
Ex. 1: Find x.
B.
A.
76
81
72
43
x
38
x
148