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° .

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

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 of5.

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°

GUIDED PRACTICE for Examples 4 and 5

SOLUTION

(Proved from above sum)

By the definition of congruence, whatadditional information is needed toknow that

5.

NDC NSR.

CN NR, CDN NSR, DCN NRS

Given :

NDC NSR.Proved :

GUIDED PRACTICE for Examples 4 and 5

STATEMENT REASON

Given

Given

CDN NSR

DCN NRS

Therefore DC RS, DN SN as angles are congruent their sides are congruent.