Geometry/Trig 2 Name: ____________________________________

1. Geometry/Trig 2 Name: ____________________________________ 2.3 Proving Theorems Homework Date: ____________________________________ Directions: In this homework, you will see proofs practiced in Section 2.2. You will also see proofs that incorporate the Midpoint Theorem and the Angle Bisector Theorem. NOTE: You are not proving these theorems, so you may use them as your justifications. Proof 1 HINT: In this example, you are going to write the two givens separately. You need to decide which should go in statement 1 and which should go in statement 4. C A T Given: CT = DG; AT = DO Prove: CA = OG O G D Statements Reasons 1.) ______________________________ 2.) ____ + ____ = CT ____ + ____ = DG 3.) CA + AT = DO + OG 4.) ______________________________ 5.) ______________________________ 1.) Given 2.) _____________________________ 3.) ______________________________ 4.) Given 5.) ______________________________ Proof 2 M A T H Given: MA = TH Prove: MT = AH Statements Reasons 1.) ______________________________ 2.) MA + AT = AT + TH 3.) ____ + ____ = MT ____ + ____ = AH 4.) ______________________________ 1.) ______________________________ 2.) ______________________________ 3.) ______________________________ 4.) ______________________________

2. Proof 3 K L M Given: mÐJXL = mÐKXM Prove: mÐ1 = mÐ3 J 1 3 2 X Statements Reasons 1.) _______________________________ 2.) mÐ1 + mÐ2 = mÐJXL mÐ2 + mÐ3 = mÐKXM 3.) _______________________________ 4.) _______________________________ 1.) _______________________________ 2.) _______________________________ 3.) Substitution 4.) _______________________________ Proof 4 A E C Given: BC is the bisector of ABD FG is the bisector of EFH mABC = mEFG Prove: mABD = mEFH G B F D H Statements Reasons 1.) ______________________________ ______________________________ 2.) mABC = ½mABD mEFG = ½mEFH 3.) ______________________________ 4.) ½mABD = ½mEFH 5.) ______________________________ 1.) Given 2.) _______________________________ 3.) Given 4.) _______________________________ 5.) _______________________________