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Triangle ABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD = AB(see Fig. 7.34). Show that angle BCD is a right angle. |
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Answer» - • AB = AC • AD = AB That is AC = AB = AD To Prove :-ΔBCD = 90° PROOF :- In ΔABC , AB = AC Therefore, ΔABC = ΔACB [ Angles opposite to equal sides are equal ]Now, In ΔACD AC = AD ΔADC = ΔACD [ Angles Opposite to equal sides are equal ] Now, In ΔBCD ΔABC + ΔBCD + ΔBDC = 180° eq( 1 )[ Angle SUM property ] ΔACB + ΔBCD + ΔACD = 180° eq( 2 )[ Angle Sum Property ] Therefore, From ( 1 ) and ( 2 )( ΔACB + ΔACD) + ΔBCD = 180° ΔBCD + ΔBCD = 180° 2ΔBCD = 180° ΔBCD = 180° / 2 ΔBCD = 90° Hence, Proved |
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