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Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples Name the parts of their sides that DFG and EHG share. Identify the overlapping triangles. Parts of sides DG and EG are shared by DFG and EHG. These parts are HG and FG, respectively. Quick Check HELP GEOMETRY Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples Write a Plan for Proof that does not use overlapping triangles. Given: ZXW YWX, ZWX Prove: ZW YX YXW Label point M where ZX intersects WY, as shown in the diagram. ZW YX by CPCTC if ZWM YXM. You can prove these triangles congruent using ASA as follows: Look at MWX. MW Theorem. MX by the Converse of the Isosceles Triangle 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. Quick Check HELP GEOMETRY Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples 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. Proof: You are given XW YZ. Because XWZ and YZW are right angles, XWZ YZW. WZ ZW, by the Reflexive Property of Congruence. Therefore, XWZ YZW by SAS. WXZ ZYW by CPCTC, and XPW YPZ because vertical angles are congruent. Therefore, XPW YPZ by AAS. Quick Check HELP GEOMETRY Using Corresponding Parts of Congruent Triangles LESSON 4-7 Additional Examples Given: CA CE, BA DE Write a two-column proof to show that CBE Proof: Statements Plan: CBE CDA by CPCTC if CBE This congruence holds by SAS if CB CD. Reasons 1. BCE DCA 2. CA CE, BA DE 3. CA = CE, BA = DE 4. CA – BA = CE – DE 5. CA – BA = CB, CE – DE = CD 6. CB = CD 7. CB CD 8. CBE CDA 9. CBE CDA HELP CDA. CDA. 1. Reflexive Property of Congruence 2. Given 3. Congruent sides have equal measure. 4. Subtraction Property of Equality 5. Segment Addition Postulate 6. Substitution 7. Definition of congruence 8. SAS 9. CPCTC Quick Check GEOMETRY