Answer:
See below.
Step-by-step explanation:
You're supposed to follow directions. That means you examine the figure to see if it contains information that will justify the offered statement. You are not to make any assumptions based on appearances.
1. AE║BC — false. There is nothing in the diagram that shows AE to be perpendicular to AB, and there are no markings indicating AE║BC.
2. AB⊥BC — true. The right-angle mark where the segments meet at point B indicates these segments are perpendicular.
3. m∠ECB=90° — false. There is nothing in the diagram that shows EC to be perpendicular to BC, and there are no markings indicating EC║AB.
4. ∠BEC is supplementary to ∠ECB — false. These are two of three interior angles of ΔBCE. There is nothing to indicate that the third angle, ∠CBE, has a measure of 0°.
5. C is the midpoint of BD — false. BC is not marked as being congruent to CD.
6. ∠BCE and ∠ECD are a linear pair — true. Point C is on line BD, so segment EC divides ∠BCD into a linear pair.
7. ∠ABE is complementary to ∠EBC — true. Together these angles form right angle ABC, so they are complementary.
