A photograph of a surfer on a surfboard is enlarged by a scale factor of 8 to make a poster. If the...
-
Upload
clyde-burns -
Category
Documents
-
view
219 -
download
6
Transcript of A photograph of a surfer on a surfboard is enlarged by a scale factor of 8 to make a poster. If the...
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
4.1 warm-up
8
4.5 Isosceles and
Equalateral TrianglesYou will
construct and justify
statement about
isosceles and equilateral triangles .
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.
Vertex
Angle
Base
Angle
Base
Angle
Leg
Leg
Base
Remember that at least two sides
are congruent
for an isosceles triangle.
Remember that all three
sides are congruent
for an equilateral triangle.
If two sides of a triangle are If two sides of a triangle are congruent, then the angles congruent, then the angles opposite those sides are opposite those sides are
congruent.congruent.
Here comes some theorems
Isosceles Triangle Theorem
BACBACBCABCA
A
B
C
If two angles of a triangle are If two angles of a triangle are congruent, then the sides congruent, then the sides opposite those angles are opposite those angles are
congruent.congruent.
Here comes some theorems
Converse of Isosceles Triangle Theorem
BABABCBC
A
B
C
The bisector of the vertex The bisector of the vertex angle of an isosceles triangle angle of an isosceles triangle is the perpendicular bisector is the perpendicular bisector
of the baseof the base
Here comes some theorems
Vertex of Isosceles Triangle Theorem
DBADBADBCDBC
A
B
CD
BDABDA909000
BDC=90BDC=9000
DADADCDC
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 W
Y
X
VT________
VX
Why ?V
U
T W
Y
X
2 ’s,
opposite sides
Here’s another one.V
U
T W
Y
X
UT________UW
Why ?V
U
T W
Y
X
2 ’s,
opposite sides
Given: KHGiven: KHKJ,KJ,
KM bisects HJKM bisects HJ
Prove: Prove: HHJJ
It’s time for a proof.
StatementStatement ReasonReason
1. Given1. KHKJ, KM bisects HJ
2. Reflexive2. KMKM
3. HMJM 3. Def of bisect
K
H M J
X
4. SSS4. KMHKMJ
5. HJ 5. CPCTC
Given: KHGiven: KHKJ,KJ,
KM bisects HJKM bisects HJ
Prove: Prove: HHJJ
It’s time for a proof.
StatementStatement ReasonReason
1. Given1. KHKJ, KM bisects HJ
2. sides congruent, then opposite angles congruent
2. HJ
K
H M J
X
HereComes
The Assignment
Worksheet 4.5
1. x=350
y=350
2. x=800
y=900
3. t=1500
4. r=450
s=450
5.x=550
y=700
z=1250
10. AD
11. GA
12. KJ
13. DC
14. BA
15. CB
6. a=1500
b=600
c=600
7. X=6
8. a=300
b=300
c=750
9. z=1200
16. 1300
17.1300
18.1300
19. 900
20. x=700
y=550
21. x=700
y=200
22. x=450
y=450