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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. BACBCA 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. BABC 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 DBADBC BDA900 BDC=900 DADC 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: KHKJ, KM bisects HJ Prove: HJ H X M J Statement Reason 1. KHKJ, KM bisects HJ 1. Given 2. KMKM 2. Reflexive 3. HMJM 3. Def of bisect 4. KMHKMJ 4. SSS 5. CPCTC 5. HJ It’s time for a proof. K Given: KHKJ, KM bisects HJ Prove: HJ H X M J Statement Reason 1. KHKJ, KM bisects HJ 1. Given 2. HJ 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