Question

diagonal of a parallelogram ABCD intersect at O. AL and CM are draw perpendicular to BD such that L and M lie on BD. is AL = CM?​

Answer 1

Step-by-step explanation:

Given, AL and CM are perpendiculars on diagonal BD. In ΔAOL and ΔCOM ∠AOL = ∠COM (vertically opposite angle) ….. (i) ∠ALO = ∠CMO = 90° (each right angle) ……. (ii) By using angle sum property ∠AOL + ∠ALO + ∠LAO = 180° ……… (iii) ∠COM + ∠CMO + ∠OCM = 180° ……. (iv) From (iii) and (iv) ∠AOL + ∠ALO + ∠LAO = ∠COM + ∠CMO + ∠OCM ∠LAO = ∠OCM (from (i) and (ii)) In ΔAOL and ΔCOM ∠ALO = ∠CMO (each right angle) AO = OC (diagonals of a parallelogram bisect each other) ∠LAO = ∠OCM (proved) So, ΔAOL is congruent to ΔCOM ∴ AL = CM (Corresponding parts of congruent triangles)Read more on Sarthaks.com - https://www.sarthaks.com/672812/parallelogramabcdintersect-alandcmare-perpendiculars-tobdsuch-thatlandmlie?show=672814#a672814