Answer:
a. Angle-angle similarity postulate (AA~)
b. Triangle CBA ~ Triangle CDE
c. x=10, y=7.5
Step-by-step explanation:
(a) You know that Angle A is congruent to Angle E. Angle BCA and Angle DCE are vertical angles, and vertical angles are congruent. The angle-angle similarity postulate says if 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar, which makes (b) Triangle CBA ~ Triangle CDE
(c) To solve for x and y, you'd have to set up proportions
x: 15/12=x/8, y: 5/8=y/12
Cross-multiply both proportions:
x - 12x=120, y - 8y=60
Divide both sides by the coefficients to get the variables by themselves:
x - 12x/12=120/12; x=10
y - 8y/8=60/8; y=7.5
