1. use the following image to answer the questions.
(a) how are the triangles similar? justify your answer with a theorem or postulate.
(b) what is the value of x? show your work.

(a) They are similar because their corresponding angles are congruent. For both triangles, we've been given 2 of the corresponding angles as congruent and therefore the 3rd corresponding angle also has to be congruent. (b) x = 5 First, let's get the length of side AC. Because the triangles are similar, the ratio, 24/32 = Z/28 will hole true. So let's solve for Z to get the length: 24/32 = Z/28 28*24/32 = Z 672/32 = Z 21 = Z Now we know the value of 3x + 6 is 21. So let's set them equal and solve for x. 3x + 6 = 21 3x = 15 x = 5

0=6x+2y+10 is equivalent to the simplified form: y= -3x - 5• parallel lines always have the same slope, different y intercept knowing this, we can say the slope, or m of the line parallel to y= -3x - 5 is -3.m= -3 hope this could !