EXAMPLE 4 Use the Third Angles Theorem Find m BDC. So, m ACD = m BDC = 105 ° by the definition of...
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Transcript of EXAMPLE 4 Use the Third Angles Theorem Find m BDC. So, m ACD = m BDC = 105 ° by the definition of...
![Page 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.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d955503460f94a7db3d/html5/thumbnails/1.jpg)
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° .
![Page 2: 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.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d955503460f94a7db3d/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d955503460f94a7db3d/html5/thumbnails/3.jpg)
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.
![Page 4: 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.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d955503460f94a7db3d/html5/thumbnails/4.jpg)
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°
![Page 5: 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.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d955503460f94a7db3d/html5/thumbnails/5.jpg)
GUIDED PRACTICE for Examples 4 and 5
By the definition of congruence, whatadditional information is needed toknow that
5.
NDC NSR.
ANSWER
DC RS and DN SN