Question

perpendicular form right angles △abd and △cbd are right triangles reason: the triangles each contain a right angle ab≅cb reason: select reason bd≅bd reason: select reason △abd≅△cbd reason: select reason answer attempt 1 out of 2

Explanation:

Step1: Identify congruent - side reason

Since $\overline{AB}\cong\overline{CB}$, this is given information about the equality of two sides of the right - triangles. The reason is "Given".

Step2: Identify congruent - side reason for $\overline{BD}\cong\overline{BD}$

The side $\overline{BD}$ is common to both $\triangle ABD$ and $\triangle CBD$. The reason for $\overline{BD}\cong\overline{BD}$ is "Reflexive Property of Congruence".

Step3: Determine triangle congruence reason

We have two right - triangles $\triangle ABD$ and $\triangle CBD$ with a pair of congruent legs ($\overline{AB}\cong\overline{CB}$) and a common hypotenuse ($\overline{BD}\cong\overline{BD}$). By the Hypotenuse - Leg (HL) Congruence Theorem, $\triangle ABD\cong\triangle CBD$. The reason for $\triangle ABD\cong\triangle CBD$ is "HL (Hypotenuse - Leg) Congruence Theorem".

Answer:

For $\overline{AB}\cong\overline{CB}$, reason: Given; For $\overline{BD}\cong\overline{BD}$, reason: Reflexive Property of Congruence; For $\triangle ABD\cong\triangle CBD$, reason: HL (Hypotenuse - Leg) Congruence Theorem.