PROOF:
1. Statement 1 is already given in the question.
2. Statement 2 is true by Division Property of Equality.
SQ/TS = 10/6 when cross-multiplied is just equal to 6SQ = 10TS.
PS/MS = 10/6 when cross-multiplied is just equal to 6PS = 10MS.
3. Statement 3 is true by Transitive Property of Equality.
The transitive property of equality states that if a = b and b = c, then a = c.
Since SQ/TS and PS/MS are both equal to 10/6, then we can say that PS/MS = SQ/TS.
4. Statement 4 is true by the definition of vertical angles. Vertical Angles are congruent.
5. Lastly, Statement 5 is true by SAS Similarity Theorem.
The corresponding sides of the two triangles are proportional to each other and have a ratio of 10/6 as stated in statements 2 and 3. Therefore, we now have two corresponding sides of each triangle that are proportional.
In addition, one included angle of these two sides as stated by Statement 4 is congruent to each other.
Since we have two sides that are proportional and an included angle that is congruent, the two triangles are similar by SAS or Side-Angle-Side Similarity Theorem.
