AMSCO'S Geometry. New York - Rye High School

130 Proving Statements in Geometry11. Given: BC hbisects ABD and mCBD mPQR.Prove: mABC mPQR12. Given: CD and AB bisect each other at E and CE BE.Prove: CD AB13. A student wrote the following proof:Given: AB > CD and AB ' BCProve: CD ' BCStatements1. AB > CD1. Given.2. AB ' BC2. Given.Reasons3. CD ' BC3. Substitution postulate.What is the error in this proof?14. A palindrome is a sequence of numbers or letters that reads the samefrom left to right as from right to left.a. Write the definition of a palindrome as a conditional statement.b. Write the converse of the conditional statement in a.c. Write the definition as a biconditional.ExplorationThe following “proof” leads to the statement that twice a number is equal to thenumber. This would mean, for example, that if b 1, then 2(1) 1, which isobviously incorrect. What is the error in the proof?Given: a bProve: b 2bStatementsReasons1. a b 1. Given.2. a 2 ab 2. Multiplication postulate.3. a 2 b 2 ab b 2 3. Subtraction postulate.4. (a b)(a b) b(a b) 4. Substitution postulate.5. a b b 5. Division postulate.6. b b b 6. Substitution postulate.7. 2b b 7. Substitution postulate.