We cannot determine without seeing the data for PRS & QRS.
My guess though would be ASA
Though it could also be SSS
When you prove a triangle is congruent to another, it can help you prove parts of the triangle congruent by checking the ratio between all sides and angles. Thank you for asking
The two legs must be corresponding sides.
Two triangles are congruent if the six elements of one triangle (three sides and three angles) are equal to the six elements of the second triangle and the two triangles have a scale factor of 1. However, in four special cases it is only necessary to match three elements to prove that two triangles are congruent. The matching of four elements is sometimes necessary, and the matching of five elements would put the matter beyond any doubt.
You would have a difficult time finding a formula to prove that statement, for two main reasons: 1). The statement is false. A triangle is never a rhombus. 2). Formulas can describe things, but they can't 'prove' things.
Theorem: A mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results. Lemma: A minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to prove a theorem. The distinction is rather arbitrary since one mathematician's major is another's minor claim. Very occasionally lemmas can take on a life of their own (Zorn's lemma, Urysohn's lemma, Burnside's lemma, Sperner's lemma).
It is a theorem, not a postulate, since it is possible to prove it. If two angles and a side of one triangle are congruent to the corresponding angles and side of another triangle then the two triangles are congruent.
ASA
Blah blah blah
Well, this will depend on the length of the sides of the triangle for what postulate or theorem you will be using.
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
SSS
AAS: If Two angles and a side opposite to one of these sides is congruent to thecorresponding angles and corresponding side, then the triangles are congruent.How Do I know? Taking Geometry right now. :)
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
HL congruence theorem
asa theorem
ASA
SAS