7.5. Proportionality Relationships http://www.ck12.org
Given: 4 BADwith−→
ACis the angle bisector of^6 BADAuxiliary lines−→
AXand←→
X D, such thatX,A,Bare
collinear and−→
AC||
←→
X D.Prove:CDBC=ADBATABLE7.4:
Statement Reason
1.−→
ACis the angle bisector of^6 BADX,A,Bare collinear
and−→
AC||
←→
X D
2.^6 BAC∼=^6 CAD
- Corresponding Angles Postulate
4.^6 CAD∼=^6 ADX
5.^6 X∼=^6 ADX - 4 X ADis isosceles
- Definition of an Isosceles Triangle
- Congruent segments are also equal
- Theorem 7-7
Review Queue Answers
- 4 AX B∼4Y X Zby AA Similarity Postulate
2.^1618 =X Z^32 ,X Z= 36
3.^1618 =AB 27 ,AB= 24
4.AY= 18 − 16 = 2 ,BZ= 36 − 32 = 4 - 162 = 324. Yes, this is a true proportion.