Answer:
Solution:
Given : In triangle ABC right angled at B.
To Prove :
Construction: Draw B D perpendicular AC.
Proof: 1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle BCD
2. = AC × DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC
3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD
4. = AC × AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD
5.
= AC (AD + DC)
6. Adding Statement 1 and Statement 2
7.
→→→Statement 3 is incorrect.It should be replaced by, Angle ABC = Angle ADB and Angle B AC = Angle BAD .
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