7. Are the two triangles similar? Show all your work done to determine this and state which similarity theorem (AA, SSS or SAS) you used to make that deterimination. Explain how you know. (2 points)
Did you use AA, SAS or SSS? Explain.
Show work
·P
14
21
M
8
Q
12
C
To determine if the two triangles are similar, we need to check if their corresponding angles are congruent and their corresponding sides are proportional.
Let's label the two triangles as triangle PMC and triangle QCJ.
Angle P is congruent to angle Q because they are vertical angles.
Angle M is congruent to angle C because they are alternate interior angles formed by a transversal cutting two parallel lines.
Angle P is not congruent to angle C, so we cannot use the AA similarity theorem.
Next, we can check if the corresponding sides are proportional using the SAS similarity theorem.
We can compare the ratios of the corresponding sides:
PM/QC = 14/12 = 7/6
MC/CJ = 21/8
The ratios are not equal, so the corresponding sides are not proportional.
Therefore, we can conclude that the two triangles are not similar.