1. GEOMETRY HELP Name the parts of their sides that DFG and EHG share. These parts are HG and FG, respectively. Parts of sides DG and EG are shared by DFG and EHG. Identify the overlapping triangles. Quick Check Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples

2. GEOMETRY HELP Write a Plan for Proof that does not use overlapping triangles. Given:  ZXW  YWX,  ZWX  YXW Prove: ZW YX You can prove these triangles congruent using ASA as follows: Label point M where ZX intersects WY, as shown in the diagram. ZW YX by CPCTC if ZWM YXM. Look at MWX. MW MX by the Converse of the Isosceles Triangle Theorem. Look again at ZWM and YXM.  ZMW  YMX because vertical angles are congruent, MW MX, and by subtraction  ZWM  YXM, so ZWM YXM by ASA. Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples Quick Check

3. GEOMETRY HELP Write a paragraph proof. Given: XW YZ,  XWZ and  YZW are right angles. Prove: XPW YPZ Plan: XPW YPZ by AAS if  WXZ  ZYW. These angles are congruent by CPCTC if XWZ YZW. These triangles are congruent by SAS. Therefore, XWZ YZW by SAS.  WXZ  ZYW by CPCTC, and  XPW  YPZ because vertical angles are congruent. Therefore, XPW YPZ by AAS. Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples Quick Check Proof: You are given XW YZ. Because  XWZ and  YZW are right angles,  XWZ  YZW. WZ ZW, by the Reflexive Property of Congruence.

4. GEOMETRY HELP Given: CA CE, BA DE Write a two-column proof to show that  CBE  CDA. 3. CA = CE, BA = DE 3. Congruent sides have equal measure. 4. CA – BA = CE – DE 4. Subtraction Property of Equality 5. CA – BA = CB,5. Segment Addition Postulate CE – DE = CD 6. CB = CD6. Substitution Plan:  CBE  CDA by CPCTC if CBE CDA. This congruence holds by SAS if CB CD. Proof: StatementsReasons 1.  BCE  DCA 1. Reflexive Property of Congruence 2. CA CE, BA DE 2. Given7. CB CD7. Definition of congruence 8. CBE CDA8. SAS 9.  CBE  CDA9. CPCTC Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples Quick Check