AMSCO'S Geometry. New York - Rye High School

124 Proving Statements in Geometry3-8 THE MULTIPLICATION AND DIVISION POSTULATESThe postulates of multiplication and division are similar to the postulates ofaddition and subtraction.The postulates in this section are stated in symbols andin words.The Multiplication PostulatePostulate 3.8If a b, and c d, then ac bd.If equals are multiplied by equals, the products are equal.When each of two equal quantities is multiplied by 2, we have a special caseof this postulate, which is stated as follows:Postulate 3.9Doubles of equal quantities are equal.The Division PostulatePostulate 3.10If a b, and c d, thena bc d (c 0 and d 0).If equals are divided by nonzero equals, the quotients are equal.When each of two equal quantities is divided by 2, we have a special case ofthis postulate, which is stated as follows:Postulate 3.11Halves of equal quantities are equal.Note: Doubles and halves of congruent segments and angles will be handled inExercise 10.Powers PostulatePostulate 3.12If a b, then a 2 b 2 .The squares of equal quantities are equal.If AB 7, then (AB) 2 (7) 2 , or (AB) 2 49.