The converse of the Angle BisectorTheorem states:In AABC, if AE meets BC at D suchthat BD:CD = BA:CA, then AD is theangle bisector of LA.Note: AB|| CEStatementsReasonsBDBA1.1.GivenCDCA2.21 22.Alt. interior Z's are3.43L43.4.ACDE O ABDA4.BDBA5.5.CDCECE =CA6.Substitution (given & step 5)6.7.AACE is isosceles7.8.1 458.22459.Substitution9.AD is the angle bisector of LA10.10.19

3. intersecting angles are equal. 4.congruent 5. corresponding angles.

e converse of the Angle Bisector eorem states: 40 AABC, if AE meets BC at D such at BD:CD = BA:CA, then AD is the ngle bisector of LA. ote: AB|| CE Statements Reasons BD BA 1. Given CD CA 2. 21L2 2. Alt. interior L's are 3. 43L4 3. 4. ACDEO ABDA 4. BD BA 5. 5. CD CE CE CA Substitution (given & step 5) 6. 6. 7. AACE is isosceles 7. 4145 8. 8. 9. Substitution 9. 2245 AD is the angle bisector of LA 10. 10. 19

e converse of the Angle Bisector eorem states: 40 AABC, if AE meets BC at D such at BD:CD = BA:CA, then AD is the ngle bisector of LA. ote: AB|| CE Statements Reasons BD BA 1. Given CD CA 2. 21L2 2. Alt. interior L's are 3. 43L4 3. 4. ACDEO ABDA 4. BD BA 5. 5. CD CE CE CA Substitution (given & step 5) 6. 6. 7. AACE is isosceles 7. 4145 8. 8. 9. Substitution 9. 2245 AD is the angle bisector of LA 10. 10. 19

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter3: Triangles

Section3.3: Isosceles Triangles

Problem 24E: In concave quadrilateral ABCD, the angle at A measures 40. ABD is isosceles, BC bisects ABD, and DC...

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