#Triangle proof
frozen garnetBOT
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If you can prove $\triangle ABD \cong \angle CBD$, then you can conclude $\overline{AB} \cong \overline{CB}$ by CPCTC
errant patioBOT
Civil Service Pigeon
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To prove this, note that you already have a pair of angles ($\angle ABD$ and $\angle CBD$) and a shared side ($\overline{BD}$)
errant patioBOT
Civil Service Pigeon
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The only thing that you haven't used so far is $\angle ADE \cong \angle CDE$
errant patioBOT
Civil Service Pigeon
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Consider how you can use this
Hint: Recall that ||supplements of congruent angles are congruent||
echo parcel
it says that These angles have already been proven to be congruent.
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I said to figure out what else you can deduce now that you know those angles are congruent
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Hint: Recall that ||supplements of congruent angles are congruent||
and I also gave you a hint here
echo parcel
what do i put next
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Hint: Recall that ||supplements of congruent angles are congruent||
I said this for a reason
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**Civil Service Pigeon**
What angles are supplementary to the angles mentioned here
echo parcel
what
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Do you know what supplementary means?
echo parcel
yes
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I'm asking you to identify what angle(s) are supplementary to angle ADE
and what angle(s) are supplementary to angle CDE
because then, we can conclude those must also be congruent for the reason I stated earlier
echo parcel
abd and bcd
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And how did you deduce that?
echo parcel
i need help
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yes
Since you know what supplementary means
Are you familiar with the common cases where supplementary angles appear?
echo parcel
no
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Are you familiar with linear pairs?
echo parcel
no please help me get the a answer
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I'm trying to help you understand the theory you need to get there, especially so you can use it for future questions
But if you're not going to work with me, then I guess that there's no reason for me to stay around
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Are you familiar with *linear pairs*?
So would you like me to explain this so you can apply it
or not
echo parcel
ok please explain
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A linear pair is defined as a pair of angles that share an adjacent side and where the other side lies along the same line
Ex. In this diagram, BC is the shared side and the other sides (AB and BD) lie along the same line AD
It's always true that angles that form a linear pair add up to 180 degrees
aka they're supplementary
So again, return to this
echo parcel
ok
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Can you identify any angles that are supplementary to ADE and/or CDE?
echo parcel
ABE