Question

In the given figure, if AB = AC, then which of the following statement(s) is/are true?

• A. $△$ABD $\cong △$ACD by RHS postulate
• B. $△$ABD $\cong △$ACD by ASA postulate
• C. BD = DC
• D. If $\angle$ABD = 60${}^{\circ }$, then, $\angle$ACD = 30${}^{\circ }$

Answer 1

Answer: (A), (C)

The correct options are
A $△$ABD $\cong △$ACD by RHS postulate
C BD = DC

In $△$ABD and $△$ACD,
$\angle$ADB = $\angle$ADC = right angle
AD = AD ( common)
AB = AC (are hypotenuse and equal)

$△$ADB $\cong △$ADC
by RHS criterion for congruency of triangles

BD = CD (corresponding parts of congruent triangles)

If $\angle$ABD = 60${}^{\circ }$, then, $\angle$ACD = 60${}^{\circ }$ (corresponding parts of congruent triangles), hence $\angle ACD\ne 30°$