Given: b is the midpoint of segment a c. segment b c is congruent to segment d e. prove: segment a b is congruent to segment d e. art: three line segments a b, b c, and d e. line segments a b and b c make a straight line. line segment d e intersects line segment b c. point d lies on upward-left direction from line segment b c. statements reasons 1. b is the midpoint of ac. given 2. ab≅bc definition of midpoint 3. bc≅de given 4. ab≅de
what is the reason for statement 4 of the two-column proof? symmetric property of equality segment congruence postulate segment addition postulate transitive property of congruence

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16