Transcript 4.2 Triangle Congruence by SSS and SAS

4.1 warm-up
A photograph of a surfer on a surfboard is
enlarged by a scale factor of 8 to make a
poster. If the surboard in the photograph is
1.5 inches long, how long is the surfboard in
the poster?
f. 8 in.
g. 12 in.
h. 18 in.
j. 96in
8
4.5
Isosceles and
Equalateral
Triangles
You will
construct and
justify
statement
about isosceles
and equilateral
You need to
remember
some things from
Chapter 3.
An isosceles triangle
has at least two
congruent sides.
An equilateral
triangle has all three
congruent sides.
Lets look at the parts of a triangle.
Remember
that at least
two sides
are
congruent
for an
isosceles
triangle.
Base
Angle
Vertex
Angle
Base
Remember
that all three
sides are
congruent
for an
equilateral
triangle.
Base
Angle
Here comes some
theorems
Isosceles Triangle Theorem
If two sides of a triangle are
congruent, then the angles
opposite those sides are
congruent.
BACBCA
B
A
C
Here comes some
theorems
Converse of Isosceles Triangle
Theorem
If two angles of a triangle are
congruent, then the sides
opposite those angles are
congruent.
BABC
B
A
C
Here comes some
theorems
Vertex of Isosceles Triangle
Theorem
The bisector of the vertex
angle of an isosceles
triangle is the perpendicular
bisector of the base
DBADBC
BDA900
BDC=900
DADC
A
B
D
C
How about some
corollaries {add ons}
If a triangle is
equilateral, then the
triangle is equiangular.
How about some
corollaries {add ons}
If a triangle is
equiangular, then the
triangle is equilateral.
Now its’ your turn.
V
U
T
Y
W
VX
VT________
X
Why ?
V
U
T
Y
W
X
2  ’s,
opposite sides 
Here’s another one.
V
U
T
Y
W
UW
UT________
X
Why ?
V
U
T
Y
W
X
2  ’s,
opposite sides 
It’s time for a proof.
K
Given: KHKJ,
KM bisects HJ
Prove: HJ
H
X
M
J
Statement
Reason
1. KHKJ, KM bisects HJ
1. Given
2. KMKM
2. Reflexive
3. HMJM
3. Def of bisect
4. KMHKMJ
4. SSS
5. CPCTC
5. HJ
It’s time for a proof.
K
Given: KHKJ,
KM bisects HJ
Prove: HJ
H
X
M
J
Statement
Reason
1. KHKJ, KM bisects HJ
1. Given
2. HJ
2. sides congruent,
then opposite angles
congruent
Here
Comes
The
Assignment
Worksheet 4.5
a=1500
10. AD
16. 1300
y=350
b=600
11. GA
17.1300
2. x=800
c=600
12. KJ
18.1300
7. X=6
13. DC
19. 900
8. a=300
14. BA
20. x=700
15. CB
y=550
1.
x=350
y=900
3. t=1500
4.
6.
r=450
b=300
s=450
c=750
5.x=550
y=700
z=1250
9. z=1200
21. x=700
y=200
22. x=450
y=450