A student solves the following equation for all possible values of x: StartFraction 8 Over x 2 EndFraction = StartFraction 2 Over x minus 4 EndFraction His solution is as follows: Step 1: 8(x – 4) = 2(x 2) Step 2: 4(x – 4) = (x 2) Step 3: 4x – 16 = x 2 Step 4: 3x = 18 Step 5: x = 6 He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0. Which best describes the reasonableness of the student’s solution? His solution for x is correct and his explanation of the extraneous solution is reasonable. His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x. His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x. His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

In δabc shown below, bd over ba equals be over bc: triangle abc with segment de intersecting sides ab and bc respectively. the following flowchart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side: top path, by given the ratio of line segments bd to ba is equal to the ratio of line segments be to bc. by space labeled by 2, space labeled by 1 occurs. by corresponding parts of similar triangles, angle bde is congruent to angle bac. by converse of the corresponding angles postulate, line segment de is parallel to line segment ac. bottom path, by reflexive property of quality, angle b is congruent to angle b. by space labeled by 2, space labeled by 1 occurs. by corresponding parts of similar triangles, angle bde is congruent to angle bac. by converse of the corresponding angles postulate, line segment de is parallel to line segment ac. which reason can be used to fill in the numbered blank space? 1. δabc ~ δbed 2. side-angle-side similarity postulate 1. δabc ~ δbed 2. side-side-side similarity theorem 1. δabc ~ δdbe 2. side-angle-side similarity postulate 1. δabc ~ δdbe 2. side-side-side similarity theorem