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