please give examples of working models on SAS congruence
Sure! "SAS congruence" refers to the criteria for proving that two triangles are congruent. SAS stands for "side-angle-side," meaning that if two triangles have the same length for one side, the same measure for one angle, and the same length for another side, then the two triangles are congruent.
Here are a few examples of working models using SAS congruence:
Example 1:
Consider two triangles, ΔABC and ΔPQR.
Given:
AB = PQ
∠ABC = ∠PQR
BC = QR
To show that the triangles are congruent using SAS congruence, we need to match each corresponding side and angle:
Side AB = Side PQ (given)
Angle ABC = Angle PQR (given)
Side BC = Side QR (given)
Since all three sets of corresponding sides and angles are equal, we can conclude that ΔABC ≅ ΔPQR.
Example 2:
Consider two triangles, ΔDEF and ΔJKL.
Given:
DE = JK
∠E = ∠K
EF = LK
To show that the triangles are congruent using SAS congruence, we need to match each corresponding side and angle:
Side DE = Side JK (given)
Angle E = Angle K (given)
Side EF = Side LK (given)
Since all three sets of corresponding sides and angles are equal, we can conclude that ΔDEF ≅ ΔJKL.
Remember, when using SAS congruence, it is important to match both sides and angles. If all three pairs of corresponding sides and angles are equal, then the triangles are proven to be congruent.
I hope this helps clarify how to work with SAS congruence in triangles!