Geometry Agenda
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Transcript of Geometry Agenda
Geometry Agenda Warm up
Mapquest 2
Interior/Exterior Triangle Angles Notes Practice
Session 5 Warm-upBegin at the word “Today”. Every Time you move, write down the word(s) upon which
you land.
Today
GO
JAGS!
is
homecoming!
school
Spirit!
your
Show
1. Move to the corresponding angle.2. Move to the vertical angle.3. Move to the supplementary angle.4. Move to the alternate interior angle.
.5. Move to the vertical angle6. Move to the alternate exterior angle.
7. Move to the consecutive exterior angle.
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 & AnglesTriangles & Angles
September 27, 2013September 27, 2013
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
If , thenACAB CB
Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
If , thenCB ACAB
EXAMPLE 1 Apply the Base Angles Theorem
P
R
Q
(30)°
Find the measures of the angles.SOLUTION
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.
EXAMPLE 2 Apply the Base Angles Theorem
P
R
Q(48)°
Find the measures of the angles.
EXAMPLE 3 Apply the Base Angles Theorem
P
R
Q(62)°
Find the measures of the angles.
EXAMPLE 4 Apply the Base Angles Theorem
Find the value of x. Then find the measure of each angle.
P
RQ(20x-4)°
(12x+20)° SOLUTION
Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 12x + 20 = 20x – 4
20 = 8x – 4
24 = 8x
3 = x
Plugging back in,
And since there must be 180 degrees in the triangle,
564)3(20
5620)3(12
Rm
Pm
685656180Qm
LEG
LEG
HYPOTENUSE
Interior Angles Exterior Angles
Triangle Sum TheoremTriangle Sum TheoremThe measures of the three interior angles
in a triangle add up to be 180º.
x°
y° z°
x + y + z = 180°
54°
67°
R
S T
m R + m S + m T = 180º 54º + 67º + m T = 180º
121º + m T = 180º
m T = 59º
Find in RST.m T
85° x°55°
y°
A
B
C
D
E m D + m DCE + m E = 180º55º + 85º + y = 180º
140º + y = 180º
y = 40º
Find the value of each variable in DCE
Find the value of each variable.
x = 50º
x°
x° 43°
57°
Find the value of each variable.
x = 22º
(6x – 7)°43°55°
28°
(40 + y)°
y = 57º
Find the value of each variable.
x = 103º
62°
50°
50°
53°
x°
The measure of the exterior angle is equal to the sum of two nonadjacent interior angles
1
2 3
m1+m2 =m3
Exterior Angle TheoremExterior Angle Theorem
x
43
3881
148
72
x76
Ex. 1: Find x.
A. B.