Question

Activity 2: Find MeFind the missing pair of congruent parts necessary to prove that the pair of triangles is congruent by the given postulate.

Answer 1

The congruence required is:

`\triangle ABD\cong\triangle CBD`

a. The first postulate is the SAS congruence postulate. It states that:

The given pair of congruent parts are:

`\overline{AD}\cong\overline{CD},\angle A\cong\angle C`

A pair of congruent sides is given and a pair of congruent angles is given.

From the postulate, the missing pair of congruent parts has to be a pair of congruent sides that will make the given pair of congruent angles included (sandwiched between the congruent sides).

Hence, the required pair of congruent sides is:

`\overline{AB}\cong\overline{CB}`

b. The second postulate is the ASA congruence postulate:

The given congruent parts are:

`\angle ABD\cong\angle CBD,\overline{DB}\cong\overline{DB}`

A pair of congruent angles and a pair of congruent sides are given. From the postulate, the missing pair has to be a pair of congruent angles that will make the given pair of sides included.

Hence, the required pair of congruent angles is:

`\angle ADB\cong\angle CDB`

c. The third postulate is the SSS congruence postulate:

The given congruent pairs are:

`\overline{AD}\cong\overline{CD},\overline{AB}\cong\overline{CB}`

Since two pairs of congruent sides are given, from the postulate, the pair of the third side must be congruent.

Hence, the missing pair of congruent sides is:

`\overline{DB}\cong\overline{DB}`

Answers:

`\begin{gathered} a\text{.}\; \overline{AB}\cong\overline{CB} \\ b\text{.}\; \angle ADB\cong\angle CDB \\ c\text{.}\; \overline{DB}\cong\overline{DB} \end{gathered}`