Statement reason 1. let points a, b, and c form a triangle. given 2. let be a line passing through b, parallel to , with angles as labeled. defining a parallel line and labeling angles 3. 4. , and . congruent angles have equal measures. 5. angle addition and definition of a straight angle 6. substitution what is the missing step in this proof? statement: , and . reason: alternate interior angles theorem statement: is parallel to . reason: is a transversal cutting and . statement: , and . reason: alternate interior angles theorem statement: , and . reason: and , and and are pairs of supplementary angles.

Drag and drop a statement or reason to each box to complete the proof. statement reason △abc , de⎯⎯⎯⎯⎯∥ac⎯⎯⎯⎯⎯ given corresponding angles postulate △bde∼△bac babd=bcbe polygon similarity postulate ba=bd+dabc=be+ec bd+dabd=be+ecbe substitution property of equality bdbd+dabd=bebe+ecbe addition of fractions 1+dabd=1+ecbe simplify. dabd=ecbe subtraction property of equality

Scientist: cross-sections of stalactites—calcite formations deposited on cave ceilings by seeping water—can reveal annual variations in rainfall in particular areas over hundreds and thousands of years. we often found that when—according to these cross-sections—drought occurred in a particular area, it coincided with the collapse of an ancient society in that area. i hypothesize that drought reduced agricultural productivity in these areas, thereby leaving these societies without the resources needed to handle internal stresses and external threats. which of the following, if true, would most weaken the support for the scientist's hypothesis? a. many droughts indicated in the cross-sections of stalactites do not correspond with the collapse of a society in that area. b. information from the cross-sections of stalactites alone cannot reveal the level of agricultural output in an area at a particular time. c. most of the societies that collapsed during droughts did so when internal power struggles coincided with military raids from neighboring societies. d. most of the societies that collapsed during droughts maintained large stockpiles of food and water at the time of their collapse. e. information from stalactites also suggests that the collapse of some societies coincided with periods of abnormally high rainfall.

One reason that madrid became the capital of spain is because of its