Is it true that ∆AEB ≅ ∆DEC? How do you know?
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Yes, ∆AEB ≅ ∆DEC by the SSS postulate.
Is it true that ∆AEC ≅ ∆DEB? How do you know?
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Yes, ∆AEC ≅ ∆DEB because of the SSS postulate (BD ≅ AC because of the segment addition postulate).
Is it true that ∆MNP ≅ ∆OPN? How do you know?
What do we need to prove congruence (other than Oompa-Loompas)?
There is not enough information to determine whether or not ∆MNP ≅ ∆OPN.
If PR bisects ∠QPS, is it true that ∆QPR ≅ ∆SPR? How do you know?
Angle bisectors split angles exactly half.
Yes, ∆QPR ≅ ∆SPR because of the SAS postulate.
Is it true that ∆ABC ≅ ∆A'B'C'? How do you know?
We can't check all the angles and sides, so we'll have to rely on either SSS or SAS.
Our congruent angle is not between our two congruent sides, so there's not enough information to figure out whether ∆ABC ≅ ∆A'B'C'. Sad face.
If ∆KLO ≅ ∆MLN, is it true that ∆KNO ≅ ∆MON? How do you know?
Congruent triangles have identical sides and angles.
Yes, ∆KNO ≅ ∆MON because of the SSS and SAS postulates.
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