Download Unit 4 Classification of Triangles

Unit 4
Classification of
Triangles
Oct 10­8:04 AM
4.1
A transformation is a change in the position, shape, or size of a figure.
Types include 1.
2.
3.
4.
Oct 4­12:18 PM
Oct 4­12:23 PM
1
Which transformations produce congruent figures?
Oct 4­12:23 PM
4.2
Types of Triangles
Classified by SIDES
• Equilateral: ___
• Isosceles: ____
• Scalene: _____
Classified by ANGLES
• Right: _____
• Obtuse: _____
• Acute:______
• Equiangular: ____
Oct 8­7:40 AM
B. Types of Triangles
Classified by SIDES
• Equilateral: all sides congruent
• Isosceles: at least 2 sides congruent
• Scalene: NO congruent sides
Classified by ANGLES
• Right: one right angle
• Obtuse: one obtuse angle
• Acute: all acute angles
• Equiangular: all angles congruent
Oct 8­7:40 AM
2
Example:
Draw an isosceles triangle. Label the triangle RST.
Mar 11­1:21 PM
III. Isosceles and Equilateral Triangles
Pull
A. Isosceles Triangle: with at least 2 sides
1. Legs: the 2 sides
2. Base: non sides
3. Vertex angle: angle between the legs
4. Base angle: angles opposite the sides
Oct 10­7:55 AM
4.3
Jul 17­10:54 AM
3
Find m<1
Jul 17­12:52 PM
Third angle theorem­ If two angles of a triangle are congruent to two angles of another triangle, then the third pair of angles are congruent.
K 4y2
J
6y2­50
Find m<K and M<J
Aug 11­9:22 AM
4.4 Congruent Triangles
I. Congruent Figures
A. Congruent polygons have congruent corresponding angles and sides.
polygon MORE polygon CASH
O
M
H
C
R
E
A
S
Oct 10­8:10 AM
4
B.
Congruent Triangles: two or more triangles with congruent corresponding angles and sides.
O
M
G
T
K
L
Oct 23­12:21 PM
D
A
F
B
C
E
parts that correspond
<A
AB
<B
AC
<C
CB
Congruence statement ABC =
_____
Oct 10­7:55 AM
If ABR TRB
Then BAR _______
TR = _______
m R = ____________
F
M
G
E
Write a congruence statement for the triangles
K
Oct 8­9:48 AM
5
Oct 8­11:17 AM
4.5 & 4.6
Ways to prove triangles congruent
Explore and discover the combinations
http://nlvm.usu.edu/en/nav/frames_asid_165_g_1_t_3.html
make sure you use Internet explorer
Oct 5­10:53 AM
II. Proving Congruent Triangle
A. Side­Side­Side Theorem (SSS)
Oct 10­7:54 AM
6
B. Side­Angle­Side Theorem (SAS)
U
B
C
A
V
L
Oct 24­9:04 AM
M
W
Q
Z
P
MQW
Pull
PQW
by .... ________
Oct 24­9:17 AM
C. Angle­Side­Angle Theorem (ASA)
H
B
2
A
40
60
2
W
C
40
60
T
Oct 10­7:54 AM
7
D. Angle­Angle­Side Theorem (AAS)
B
C
A
O
T
P
Oct 10­7:54 AM
Mar 15­10:09 AM
Mar 15­7:07 AM
8
Mar 15­7:11 AM
Mar 15­7:15 AM
hy
p
leg
ote
nu
s
e
leg
Oct 10­7:57 AM
9
Mar 24­12:37 PM
HA, LL , LA and HL
Oct 10­7:57 AM
Oct 11­6:48 AM
10
Warm­up
Given: F H
FG // JH
#2
G
F
Prove: FGJ HJG
H
J
Oct 10­7:55 AM
Warm­up
#2
Given: F H
FG // JH
G
F
Prove: FGJ HJG
H
J
Oct 10­7:55 AM
#3
C
Given: OHL and OHC are right
OH bisects CL
Prove: OHC OHL
H
O
L
Oct 10­7:55 AM
11
#3
Given: OHL and OHC are right
OH bisects CL
C
H
Prove: OHC OHL
O
L
Oct 10­7:55 AM
U
#4
Given: BU // YN
BY // UN
Prove: BUN NYB
2
B
1
6
3
4
N
5
Y
Oct 10­7:55 AM
U
#4
Given: BU // YN
BY // UN
Prove: BUN NYB
2
B
1
6
3
4
N
5
Y
Oct 10­7:55 AM
12
4.7 If two triangles are congruent, then all corresponding parts are congruent.
CPCTC­ Corresponding Parts of Congruent Triangles are Congruent
Aug 11­9:49 AM
#5
P
Given: P R
AT bisects PTR
Prove: PA AR
R
A
T
Oct 10­7:55 AM
#5
Given: P R
AT bisects PTR
Prove: PA AR
R
P
A
T
Oct 10­7:55 AM
13
#6
S
Given: KI SN
KI bisects SN
Prove: S N
I
K
N
Oct 10­7:55 AM
S
#6
Given: KI SN
KI bisects SN
Prove: S N
I
K
N
Oct 10­7:55 AM
Quadratic equations on pg 278 and then skip 4.8
Oct 8­11:25 AM
14
4.9
III. Isosceles and Equilateral Triangles
Pull
A. Isosceles Triangle: with at least 2 sides
1. Legs: the 2 sides
2. Base: non sides
3. Vertex angle: sides of the are the 2 legs
4. Base angle: 1 side of the is the base
Oct 5­11:18 AM
Oct 5­11:19 AM
B. Theorems
< opposite sides are Isosceles Triangle Theorem
sides opposite < are Converse of the Isosceles Theorem
Oct 30­8:19 PM
15
Find <T
Oct 18­11:20 AM
find x or t
Oct 18­11:28 AM
B
#7
1 2
A
D
C
Oct 10­7:55 AM
16
B
#7
1 2
A
D
C
Oct 10­7:55 AM
Oct 31­1:32 PM
Mar 24­9:27 AM
17
C
12
A
B
Given: D is the midpoint of AB
<A = <B
Prove: <1 = <2
Oct 21­10:20 AM
Mar 24­9:29 AM
1.
2.
Oct 19­7:39 AM
18
3.
4.
Oct 30­8:32 PM
Given:
Prove:
Oct 10­7:57 AM
Given:
Prove:
Oct 10­7:57 AM
19
Given:
Prove:
Oct 10­7:57 AM
Given:
Prove:
Oct 10­7:57 AM
Warm­ up
Oct 10­7:57 AM
20
2.
Oct 31­2:43 PM
3.
Oct 31­2:43 PM
Given:
Prove:
Oct 10­7:57 AM
21
Given:
Prove:
Oct 10­7:57 AM
Oct 31­2:45 PM
E
R
G
A
T
Oct 23­8:04 AM
22
E
R
A
G
T
Oct 23­8:05 AM
D
B
2
1
3
C
E
4
6
5
A
F
Oct 23­8:04 AM
R
#1
P
E
O
V
Oct 10­7:54 AM
23
R
#1
P
E
O
V
Oct 10­7:54 AM
24