1. EXAMPLE 4 Use the Third Angles Theorem Find m BDC. So, m ACD = m BDC = 105° by the definition of congruent angles. ANSWER SOLUTION A B and ADC BCD, so by the Third Angles Theorem, ACD BDC. By the Triangle Sum Theorem, m ACD = 180° – 45° – 30° = 105°.

2. EXAMPLE 5 Prove that triangles are congruent Plan for Proof AC AC. a. Use the Reflexive Property to show that b. Use the Third Angles Theorem to show that B D Write a proof. GIVEN AD CB, DC AB ACD CAB, CAD ACB PROVE ACD CAB

3. EXAMPLE 5 Prove that triangles are congruent Plan in Action 1. Given 2. Reflexive Property of Congruence STATEMENTS REASONS 3. Given 4. Third Angles Theorem 1. AD CB, DC BA 2. a. AC AC. 3. ACD CAB, CAD ACB 4. b. B D 5. ACD CAB Definition of 5.

4. GUIDED PRACTICE for Examples 4 and 5 SOLUTION 4. DCN. In the diagram, what is m CDN NSR, DNC SNR then the third angles are also congruent NRS DCN = 75°

5. GUIDED PRACTICE for Examples 4 and 5 SOLUTION (Proved from above sum) By the definition of congruence, what additional information is needed to know that 5. NDC NSR. CN NR, CDN NSR, DCN NRS Given : NDC NSR.Proved :

6. GUIDED PRACTICE for Examples 4 and 5 STATEMENTREASON Given CDN NSR DCN NRS Therefore DC RS, DN SN as angles are congruent their sides are congruent.