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 Triangles You 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 L e g L e g 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 congruent, then the angles opposite those sides are congruent. Here comes some theorems Isosceles Triangle Theorem BACBCA A B C

If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Here comes some theorems Converse of Isosceles Triangle Theorem BABC A B C

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base Vertex of Isosceles Triangle Theorem DBADBC A B C D BDA900 BDC=900 DADC

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: KHKJ, KM bisects HJ Prove: HJ It’s time for a proof. StatementReason 1. Given1. KH  KJ, KM bisects HJ 2. Reflexive 2. KM  KM 3. HM  JM 3. Def of bisect K H M J X 4. SSS 4.  KMH  KMJ 5.  H  J 5. CPCTC

Given: KHKJ, KM bisects HJ Prove: HJ It’s time for a proof. StatementReason 1. Given1. KH  KJ, KM bisects HJ 2. sides congruent, then opposite angles congruent 2.  H  J K H M J X

Here Comes The Assignment Worksheet 4.5

1. x=35 0 y= x=80 0 y= t= r=45 0 s= x=55 0 y=70 0 z= AD 11. GA 12. KJ 13. DC 14. BA 15. CB 6. a=150 0 b=60 0 c= X=6 8. a=30 0 b=30 0 c= z= x=70 0 y= x=70 0 y= x=45 0 y=45 0