1) The order of the letters is important. Corresponding angles are ones that have corresponding letters in the same order.
The appropriate choice is the 2nd one ...
∠HDG ≅ ∠HFE
2) The triangle is isosceles. You know that because the base angles T and X are marked as congruent. This means the side lengths are the same.
TV = VX
10x - 26 = 5x + 9
5x = 35 . . . . . . . . . . add 26-5x
x = 7
The appropriate choice is the 3rd one ...
7
3) It can help to draw a picture. Check to see if each of the offered choices is met by the given information.
• HL : yes. XZ is the L, YZ and YW are the H. The angles at X are right angles.
• AAS : yes. The angles at X and Y and the sides YW and YZ are given as congruent.
• ASA : yes. The angles at X and Y and the side between them XY are congruent.
• SAS : yes. The side XY, the angles at Y and the sides YW and YZ are congruent.
• SSS : no. The sides XW and XZ are not given as congruent.
The appropriate choice is the 4th one ...
HL, AAS, ASA, and SAS
4) You are given sides CB and CD as congruent, and you know side CA is congruent to itself, so you need the angles between them, at C to be congruent.
The appropriate choice is the 2nd one ...
AC ⊥ BD
5) You know the triangles are right triangles and the hypotenuse QS is congruent to itself. Given that one of the legs is also congruent to the one it corresponds to, the conditions are met for the HL theorem.
The appropriate choice is the 1st one ...
HL Theorem
