Based only on the information given in the diagram, which congruence theorems could be given as reasons why...

Question

Based only on the information given in the diagram, which congruence theorems could be given as reasons why CDE OPQ?

Here is the link to the triangle-
http://i131.photobucket.com/albums/p285/pickapet1/6523d5be-e8ba-44a3-9eb4-560b06940cd.gif

A. AAS
B. LA
C. LL
D. HL
E. SAS
F. ASA

Answer 1

AAS since you have two angles and one side.

LA (never heard of it but if it's actually a theorem then yes. It makes sense in right triangles)

LL (same as LA)

HL since the hypotenuse and the leg are congruent.

SAS CAN be used BUT only if you're going to prove that the sides CE and OQ are congruent or the angles D and P are congruent. You cannot directly apply this.

ASA CAN be used BUT, as with SAS, can only be used if you prove that either the sides CE and OQ are congruent or the angles D and P are congruent. You cannot directly apply this.

Answer 2

AAS, HL, and ASA

AAS because you have 2 angle and a side = two angles and a side. Hence the third angles must also be equal. This is just the same as ASA

HL because Hypotenus and leg of one right triangle is equal to hypotenuse an leg of another. Since this is true, the ing legs must be equal by Pythgorean Theorem so it is same as SSS

Answer 3

Hl, LA, and AAS

Answer 4

It's LA and AAS according to apex.