Question

जर दोन समांतर रेषांना एका छेदिकेने छेदले असता तयार होणाऱ्या व्युत्क्रम कोनांमधील संबंध लिहा. / If a transversal intersects two parallel lines then state the relation between alternate angles

Answer 1

Answer:

जर दोन समांतर रेषांना एका छेदिकेने छेदले असता तयार होणारे कोण समान असतात ...

Answer 2

Step-by-step explanation:

• We know, The angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal are known as the alternate interior angles.
• The relation between the alternate angles formed when a transversal intersects two parallel lines is that they are always equal. This can be proved by the following:

        ⇒ Given: a║d

       ⇒ To Prove: $\angle 4=\angle 5\ and\ \angle 3=\angle6$

       ⇒ Proof: Suppose a and d are two parallel lines and l is the     transversal that intersects a and d at point P and Q. (Refer the figure)

              ⇒ From the properties of the parallel line, we know if a transversal cuts any two parallel lines, the corresponding angles and vertically opposite angles are equal to each other. Therefore,  

                   $\angle 2=\angle5$     -    (i) [Corresponding angles]  

                   $\angle2 = \angle4$     -    (ii) [Vertically opposite angles]  

             ⇒ From equation (i) and (ii), we get;  

                   $\angle 4 = \angle5$     -        [Alternate interior angles]  

             ⇒ Similarly,  

                   $\angle3 = \angle6$     -        [Alternate interior angles]  

             ⇒ Hence proved.

Therefore, Alternate interior angles are a pair of equal angles.