Triangle ABD is congruent to triangle CBD
http://curriculum.kcdistancelearning.com/courses/GEOMx-HS-A09/a/assessments/T-TrianglesUnitExam/Geometry_Unit4_Exam_36f1.gif

Question

Triangle ABD is congruent to triangle CBD
http://curriculum.kcdistancelearning.com/courses/GEOMx-HS-A09/a/assessments/T-TrianglesUnitExam/Geometry_Unit4_Exam_36f1.gif

anonymous · Answer

true or false?
Help me Plz!!!

mathmate · Answer

If two triangles have two angles and the included side congruent, the triangles are congruent.  ASA (angle-side-angle).

anonymous · Answer

so Its true

mathmate · Answer

Explain why it is true.

mathstudent55 · Answer

The triangles are congruent but not by ASA.

anonymous · Answer

Because it is a theorem

mathstudent55 · Answer

Which ways of proving two triangles congruent do you know?

mathmate · Answer

@methstudent55: if two triangles have two angle congruent, the third is also congruent.

anonymous · Answer

SAS

mathmate · Answer

@mathstudent55: if two triangles have two angle congruent, the third is also congruent.
It is not SAS because we only have one common side, and we do not know congruence of the other sides.

mathstudent55 · Answer

@mathmate You're correct. You can do it by ASA by first stating that the third angles are congruent, but there is a quicker way of doing it that does not require that extra step.

anonymous · Answer

WAIT so its true

mathmate · Answer

It still takes an extra step.

mathstudent55 · Answer

There is a way that just by looking you can immediately conclude the triangles are congruent with out any extra steps.

mathmate · Answer

To prove by SAS, you need to show that one other pair of sides are congruent.

anonymous · Answer

o its false because not much information, right?

mathmate · Answer

@ DorelTibi: sorry that we are discussing the semantics of things, but are you able to show that the triangles are congruent?

mathstudent55 · Answer

It's not SAS. We don't have info on two sides. We only know about the side in common.

mathstudent55 · Answer

Here it is: AAS. If two angles of a triangle and a not included side are congruent to corresponding parts of another triangle, the triangles are congruent.

mathmate · Answer

In fact, AAS is the equivalent of ASA, since when two angles are congruent, then congruence of any other corresponding side is sufficient to show congruence.  Equivalence means that all AAS cases can be shown to be ASA and vice-versa.

mathmate · Answer

Indeed, AAS is easier.

mathstudent55 · Answer

In the end, if you do it by ASA, you need to show BD is congr to itself and <s CDB and ADB are congruent.
If you do it by AAS, you only need to show BD is congr to itself. 
So either way you need one extra step or two extra steps before the conlcusion.