Opposite sides of parallelogram

Concept wise

### Transcript

Example 3 ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD AB. Show that DAC = BCA and Given: ABC where AB = AC AD bisects PAC, & CD AB To prove: DAC = BCA Proof: AD bisects PAC Hence PAD = DAC = 1/2 PAC Also, given AB = AC BCA = ABC For ABC , PAC is an exterior angle So, PAC = ABC + BCA PAC = BCA + BCA PAC = 2 BCA 1/2 PAC = BCA BCA = 1/2 PAC BCA = DAC Hence proved Example 3 ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD AB .Show that (ii) ABCD is a parallelogram. In previous part we proved , DAC = BCA For lines BC , AD with transversal AC DAC & BCA are alternate interior angles and they are equal So, BC AD Now, In ABCD BC AD & AB CD Since both pairs of opposite sides of quadrilateral ABCD are parallel. ABCD is a parallelogram.

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.