Determine the missing information in the paragraph proof. Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.

Prove: Parallel lines have the same slope.

On a coordinate plane, 2 lines are shown. Line Q P goes through (w, v) and (x, z). Line Q prime P prime goes through (w + a, v + b) and (x + a, z + b).

Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to . It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.

StartFraction v minus z Over w minus x EndFraction
StartFraction w minus x Over v minus Z EndFraction
StartFraction v minus z + b Over x minus z + a EndFraction
StartFraction w minus x + a Over v minus z + b EndFraction

Study guide for unit 2 ~ lesson 3 ,4, & 5 test, thursday, january 24th lesson 3 vocabulary erosion - deposition - landform- weathering- short answers 1. how do volcanic islands form? 2.why is deposition likely to occur outside a river bend? 3. in what conditions does soil form fastest? 4. which 2 earth’s systems interact to form a coral island? 5. a beach growing in size is most likely the result of 6. which type of islands are formed when a chunk of land breaks off from a larger landmass? long answers explain how plants can grow in small cracks of rock that do not appear to contain soil. lesson 4 vocabulary pollution - toxic - short answers 1. most farmers pollute soil by purposefully adding 2. what is the benefit of contour plowing? . 3. using nuclear power to produce electricity can cause water pollution by 4. why do scientists predict humans will run out of fossil fuels someday? 5.farmer spray crops with fertilizer and weed killer to the crops grow. how might this affect the hydrosphere? list two different ways you use fossil fuels. 1- 2- what are two other energy sources scientists and engineers are researching? 1- 2- lesson 5 vocabulary decompose- recycling - short answers 1. which of earth’s systems do you interact with when you wash your hands? 2. which of earth’s systems is polluted by exhaust gases from buses pollute? 3. why is it important to dispose of electronic devices properly? 4. where do people interact with all four of earth’s systems?