Given the above, which method would you use to prove ABD ≅ ACD?

AAS
SSS
SAS
ASA

https://media.glynlyon.com/g_geo_2012/6/img_geou6a_31.gif

Question

Given the above, which method would you use to prove ABD ≅ ACD?

AAS
SSS
SAS
ASA


https://media.glynlyon.com/g_geo_2012/6/img_geou6a_31.gif

mathstudent55 · Answer

What do you know about isosceles triangles?
Specifically, because tr. ABC is isosceles, what do you know about it?
What do you know about triangle BDC because it's isosceles?

anonymous · Answer

dont know anything

mathstudent55 · Answer

Isosceles triangles have two congrunet sides.
Since triangle ABC is isosceles, which two of its sides are congruent (equal length)?

anonymous · Answer

AB and AD

mathstudent55 · Answer

No. Triangle ABC doesn't have AD as a side. Look carefully at triangle ABC and ignore AD inside.
Which two sides of triangle ABC are congruent?

anonymous · Answer

AB and AC

mathstudent55 · Answer

That's good.
Now look only at triangle BDC. Ignore everything else. Triangle BDC is also isosceles. Which two sides of triangle BDC are congruent?

anonymous · Answer

BD and DC

mathstudent55 · Answer

That is great.
Now look at the two triangles you are trying to prove congruent.
They are ABD and ACD.
AB and AC are sides of those two triangles and they're congruent.
BD and DC are also sides of those triangles and they are congruent.
AD is also a side of both triangles. AD is congruent to itself by the reflexive property.
So you have 3 sides of one triangle congruent to three sides of another triangle, that means the triangles are congruent by Side-Side-Side, or simply SSS.