Question

PLEASE HELP!!

Answer 1

Answer:

∆GAS ≅ △IOL By rule ASA, AAS

Step-by-step explanation:

By looking at the triangle, you can see two little quarter-circle things inside the triangle (I don't know what they are called). That means it has 2 angles.  We already know that it can't be SSS or SAS because we have 2 angles, as I said.

If you look at the triangle's sides, you can see that there is a side with a dash on it. That means that it is a side in ASA, AAS, etc. So there we go. We've figured it out. There is one side and two angles.  Therefore, our answer is ASA or AAS

Answer 2

Answer:

ΔGAS ≅ ΔIOL By the Angle-Angle-Side (AAS) rule of congruency

Step-by-step explanation:

The given information are;

Statement                                  ${}$                               Reason

Segment $\overline {SA}$ is congruent to $\overline {OL}$              ${}$As shown in the diagram provided

∠SAG is congruent to ∠LOI               ${}$       As shown  in the diagram provided

∠SGA is congruent to ∠LIO               ${}$       As shown  in the diagram provided

Therefore, ΔGAS ≅ ΔIOL By the Angle-Angle-Side (AAS) rule of congruency

Given that the the number of interior angles of triangle = 3 and the sum of the interior angles of a triangle = 180°, the third angle can be defined by specifying the measure of two of the angles

Therefore, the Angle-Angle (AA) rule of similarity can be used to prove the congruency of two triangles when they have one side of each triangle which are congruent.