AMSCO'S Geometry. New York - Rye High School

The Substitution Postulate 11511. Explain why the following proof is incorrect.Given: ABC with D a point on BC.Prove: ADB ADCBA D CStatementsReasons1. ADB and ADC are right angles. 1. Given (from the diagram).2. mADB 90 and mADC 90. 2. A right angle is an angle whose degreemeasure is 90.3. mADB mADC 3. Transitive property of equality.4. ADB ADC 4. If two angles have the same measure,then they are congruent.Hands-On ActivityWorking with a partner: a. Determine the definitions and postulates that can be used with the givenstatement to write a proof. b. Write a proof in two-column form.Given: ABC and BCD are equilateral.Prove: AB 5 CDACDB3-6 THE SUBSTITUTION POSTULATEThe substitution postulate allows us to replace one quantity, number, or measurewith its equal. The substitution postulate is stated in words as follows:Postulate 3.4A quantity may be substituted for its equal in any statement of equality.From x y and y 8, we can conclude that x 8. This is an example of thetransitive property of equality, but we can also say that we have used the substitutionproperty by substituting 8 for y in the equation x y.