Question

assume that the set of conditionals is true. use the conditionals to write a true conditional. if you cannot write a true conditional, explain why. if $overrightarrow{bd}$ bisects $angle abc$, then $angle abdcongangle dbc$. if $angle abdcongangle dbc$, then $mangle abd = mangle dbc$. choose the correct answer below. a. it can be concluded that if $mangle abd = mangle dbc$, then $overrightarrow{bd}$ bisects $angle abc$. b. it can be concluded that if $overrightarrow{bd}$ bisects $angle abc$, then $mangle abd = mangle dbc$. c. it is not possible to write a true conditional because the hypothesis of one conditional is not the conclusion of the other conditional. d. it is not possible to write a true conditional because the conditionals do not have the same hypotheses.

Explanation:

Step1: Identify the given conditionals

We have: If $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD\cong\angle DBC$ and If $\angle ABD\cong\angle DBC$, then $m\angle ABD = m\angle DBC$.

Step2: Use the law of syllogism

The law of syllogism states that if $p
ightarrow q$ and $q
ightarrow r$, then $p
ightarrow r$. Here, $p$ is “$\overrightarrow{BD}$ bisects $\angle ABC$”, $q$ is “$\angle ABD\cong\angle DBC$” and $r$ is “$m\angle ABD = m\angle DBC$”.

Answer:

B. It can be concluded that if $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABD = m\angle DBC$