Question

c204
are the triangles similar? if yes, state how.

a. not similar the victim was not eaten by a dinosaur (c207).
b. similar; aa similarity; \\( \triangle tme\sim\triangle sam \\) ms. mccall was teaching in the media center (c213).
c. similar; sss similarity; \\( \triangle tem\sim\triangle sam \\) the gym was not where the murder took place (c205).
d. similar; aa similarity; \\( \triangle tem\sim\triangle sam \\) mr. brundage was in the main office with a parent
(c208)

Explanation:

Step1: Check for common angles

In \(\triangle TEM\) and \(\triangle SAM\), \(\angle M\) is common to both triangles.

Step2: Check for parallel - line - induced angles

Since \(SA\parallel TE\) (indicated by the arrows), \(\angle SAM=\angle TEM\) (corresponding angles).

Step3: Apply AA similarity criterion

Since two angles (\(\angle M\) and \(\angle SAM=\angle TEM\)) of \(\triangle TEM\) and \(\triangle SAM\) are equal, by the AA (Angle - Angle) similarity criterion, \(\triangle TEM\sim\triangle SAM\).

Answer:

D. Similar; AA Similarity; \(\triangle TEM\sim\triangle SAM\)