Honors Geometry 1A
Name ____________________ Honors Homework 6.3-6.4 R
Complete the following proofs. 1. Given: P Q ; RS is the angle bisector of PRQ Prove: PR QR P
Statements 1. PRQ with P Q ;
Q
S
Reasons 1.
RS is the angle bisector of PRQ 2. PRS QRS
2.
3. RS RS
3.
4. PRS QRS
4.
5. PR QR
5. CPCTC
A
2. Given: AB AD , AC BD Prove: BC DC Statements
B
C
Reasons
D
3. Given: WZ XZ , Y is the midpoint of WX Prove: 1 2 Statements
Y
W
Reasons
X
1 2 Z
Write a proof that involves overlapping triangles. 4.
C
Given: AC EC,CB CD Prove: A E
B
D F
A
Statements
E
Reasons
Questions #2-6: Write a proof that involves proving one pair of triangles congruent to prove another set of triangles congruent (and possibly their parts congruent). 5. Given: TE RI,TI RE, TDI and ROE are right 's T
Prove: TD RO
I
O D
Statements
Reasons
E
R
6.
Given: AB BC, DC BC, AC DB
D
A
Prove: AE DE E
Statements
7.
Reasons
B
C
T
Given: 1 2, 3 4 Prove: QET QEU Q
Statements
Reasons
1
3 E
4
A
G
Prove: ADC EDG F
Reasons
B
U
8. Given: AD ED , D is the midpoint of BF
Statements
2
B D
E
C
9. Given: QT PR, QT bisects PR, QT bisects VQS ,
Statements
Q
P
Prove: VQ SQ
R
Reasons
V
S
T
*Answers on Website*
Answers 1. 1. Given 2. Definition of bisect 3. Reflexive Property 4. AAS Theorem 2. Statements 1. AB AD , AC BD 2. BCA and DCA are rt. s 3. BCA and DCA are rt. s 4. AC AC 5. BCA DCA 6. BC DC 3. Statements
Reasons 1. Given 2. Definition of 3. Definition of right 4. Reflexive Property 5. HL Theorem 6. CPCTC
1. WZ XZ , Y is the midpoint of WX
Reasons 1. Given
2. WY XY
2. Definition of midpoint
3. YZ YZ 4. WZY XZY 5. 1 2
3. Reflexive Property 4. SSS Postulate 5. CPCTC
4. Statements 1. AC EC,CB CD 2. C C
Reasons 1. Given 2. Reflexive Property
3. CAD CEB
3. SAS Postulate
4. A E
4. CPCTC
5. Statements 1. TE RI,TI RE, TDI and ROE are right 's
Reasons 1. Given
2. EI IE
2. Reflexive Property
3. TEI RIE
3. SSS Postulate
4. TIE REI 5. TDI ROE
4. CPCTC 5. All right 's
6. TDI ROE 7. TD RO 6.
6. AAS Theorem 7. CPCTC
Statements
Reasons
1. AB BC, DC BC, AC DB
1. Given
2. ABC and DCB are right ' s
2. Definition of
3. ABC and DCB are right ' s
3. Definition of right
4. BC CB 5. ABC DCB
4. Reflexive Property 5. HL Theorem
6. A D 7. AEB DEC 8. AEB DEC
6. CPCTC 7. Vertical 's 8. AAS Theorem 9. CPCTC
9. AE DE 7. Statements 1. 1 2, 3 4
Reasons 1. Given
2. QB QB
2. Reflexive Property
3. QTB QUB
3. ASA Postulate
4. QU QT 5. QE QE 6. QET QEU
4. CPCTC 5. Reflexive Property 6. SAS Postulate
8. Statements
Reasons
1. AD ED , D is the midpoint of BF
1. Given
2. FD BD
2. Definition of midpoint
3. FDE BDA
3. Vertical 's
4. FED BAD 5. E A
4. SAS Postulate 5. CPCTC
6. GDE CDA 7. ADC EDG
6. Vertical 's 7. ASA Postulate
9. Statements 1. QT PR, QT bisects PR, QT bisects VQS
Reasons 1. Given
2. TQP and TQR are right ' s
2. Definition of
3. PQ RQ
3. Definition of bisect
4. TQ TQ 5. TQP TQR
4. Reflexive Property
6. TQP TQR 7. PTQ RTQ 8. VQT SQT 9. VQT SQT 10. VQ SQ
6. SAS Postulate 7. CPCTC 8. Definition of bisect 9. ASA Postulate 10. CPCTC
5. All right 's
