Question 1 - Page 12 - Congruency involving Angles - Chapter 1 Class 7 - Geometric Twins (Ganita Prakash II)

Transcript

Question 1 - Page 12 In the figure, Point O is the midpoint of AD and BC. What can one say about the lengths AB and CD? Now, possible ways to prove congruency we have learnt till now are SSS Congruency SAS Congruency ASA Congruency Here, in ∆ AOB and ∆ COD Side OA = OD Side OB = OC We do not know anything about third side But, the middle angles are equal, ∠ AOB = ∠ COD (by Vertically opposite angles) So, we can prove both these triangles congruent using SAS Congruency Finding which points match Here, ∠ AOB = ∠ COD. So point O matches with point O. Thus, Points O ⟷ O match Since OA = OD, and points O have matched. So, A and D match. Thus, Points A ⟷ D match Remaining points match Thus, Points B ⟷ C match So, we can write ∆ OAB ≅ ∆ ODC And, by Corresponding Parts of Congruent Triangles (CPCT) Corresponding sides are equal Thus, AB = DC