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## EXAMPLE 4

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**FindmBDC.**SOLUTION AB and ADCBCD, so by the Third Angles Theorem, ACDBDC. By the Triangle Sum Theorem, m ACD = 180°– 45° – 30°= 105°. So, mACD =mBDC = 105° by the definition of congruent angles. ANSWER EXAMPLE 4 Use the Third Angles Theorem**Write a proof.**GIVEN AD CB,DC AB CADACB ACDCAB, ACDCAB PROVE Use the Reflexive Property to show that AC AC. Use the Third Angles Theorem to show that BD EXAMPLE 5 Prove that triangles are congruent Plan for Proof**STATEMENTS**REASONS ,DC BA AD CB Given Reflexive Property of Congruence AC AC. ACDCAB, Given CADACB BD Third Angles Theorem ACDCAB Definition of EXAMPLE 5 Prove that triangles are congruent Plan in Action**In the diagram, what is m**DCN. CDN NSR, DNC SNRthen the third angles are also congruent NRS DCN = 75° for Examples 4 and 5 GUIDED PRACTICE SOLUTION**By the definition of congruence, what**additional information is needed to know that NDC NSR. ANSWER DC RS and DN SN for Examples 4 and 5 GUIDED PRACTICE