Download Section 4.2 Day 1 Congruence and Triangles

Week 3
Warm Up
Tell whether it is possible to draw each triangle:
1) acute scalene triangle
2) obtuse equilateral triangle
11.02.11
B
Re 1
38⁰
( 10x + 9 )⁰
A
( 7x + 1 )⁰
( 10x + 9 )º = ( 7x + 1 )º + 38º
C
( 10x + 9 )º
10x + 9 = 7x + 1 + 38
10( 10 ) + 9
10x + 9 = 7x + 39
100 + 9
3x + 9 = 39
3x = 30
x = 10
109
Geometry
4.2 Day 1
Congruence
I will identify congruent figures and
corresponding parts.
Exact same size and shape
Congruent
Not Congruent
Rule 1
Congruent figures have congruent angles and
congruent sides.
B
Ex 1
A
Q
C
P
R
∠A ≅ ∠P
≅
∠B ≅ ∠Q
≅
∠C ≅ ∠R
≅
∆ABC ≅ ∆PQR
Rule 2 List the corresponding angles in the same order so you
know which sides are congruent.
Ex 2
NPLM ≅ EFGH
LM ≅ GH
Find the value of x and y.
Rule 2 List the corresponding angles in the same order so you
know which sides are congruent.
Ex 2
NPLM ≅ EFGH
LM ≅ GH
LM = GH
8 = 2x - 3
Find the value of x and y.
Rule 2 List the corresponding angles in the same order so you
know which sides are congruent.
Ex 2
NPLM ≅ EFGH
Find the value of x and y.
LM ≅ GH
∠N ≅ ∠E
LM = GH
m∠N = m∠E
8 = 2x - 3
72 º = ( 7y + 9 )º
8 = 2x - 3
11 = 2x
5.5 = x
72 = 7y + 9
63 = 7y
9 = y
Theorem
4.3
Third Angles Theorem
If two angles of one triangle are congruent to two
angles of another triangle, then the third angles are
also congruent.
B
A
E
C
D
F
If ∠A ≅ ∠D and ∠B ≅ ∠E, then
∠C ≅ ∠F.
M
Ex 3
R
T
(2x + 30)º
55º
N
65º
L
S
∠N ≅ ∠R
m∠M = 180 - 55 - 65
∠L ≅ ∠S
m∠M = 60º
so ∠M ≅ ∠T
60 = 2x + 30
30 = 2x
15 = x
Do: 1
Name all the congruent sides.
F
E
G
B
K
Assignment:
38⁰
J
Textbook Page 205, 4 - 15 all.
H