question_answer

In the figure, AB = AC and D is the mid-point of\[\overline{BC}\].

(a) State the three pairs of equal parts in \[\Delta \]ADB and \[\Delta \]ADC

(b) Is\[\Delta ADB\cong \Delta ADC\]? Give reasons.

(c) Is \[\angle B=\angle C?\]Why?

Answer:

(a) Three pairs of equal parts in \[\Delta ADB\]and\[\Delta ADC\] are

AD = AD [Common]

AB = AC  [Given]

and DB = DC

\[\left[ \because D\text{ }is\text{ }mid-point\text{ }of\text{ }\overline{BC} \right]\]

(b) By SSS criterion of congruence,

\[\Delta ADB\cong \Delta ADC\]

(c) Yes, \[\angle \]B = \[\angle \]C   [\[\because \] Corresponding

parts of congruent triangles are equal]