Download Chapter 4: Congruent Triangles Review Determine if the following

Chapter 4: Congruent Triangles Review
Determine if the following triangles are congruent.
Diagram
Congruent
Triangles
DLMN @ D _______
(a)
or
Not congruent
DABE @ D _______
(b)
or
Not congruent
DHIJ @ D _______
(c)
or
Not congruent
DXYZ @ D _______
(d)
or
Not congruent
DRST @ D _______
(e)
or
Not congruent
DSTV @ D _______
(f)
or
Not congruent
DITR @ D _______
(g)
or
Not congruent
Explanation
Draw the following triangles. If necessary, indicate on your drawing if sides or angles are
congruent.
Scalene Obtuse Triangle
Isosceles Acute Triangle
Regular Triangle
Solve for x and y. Justify your answer with definitions, postulates, and/or theorems.
1.
2.
3.
4.
5.
6. Find the following angles. *Justify your answer with a
definition, postulate and/or theorem.
7. Find the following angles. *Justify your answer with a
definition, postulate and/or theorem.
8. Use the coordinates to determine if DABC @ DDEF .
Classify the triangles.
A(1, 3), B(4, 1), C(5, 3), D(3, -3), E(6, -5), F(7, -3).
Answer:
Justify:
a = _______
________________________
b = _______
________________________
c = _______
________________________
d = _______
________________________
e = _______
________________________
f = _______
________________________
g = _______
________________________
h = _______
________________________
k = _______
________________________
l = _______
________________________
m = _______
________________________
Answer:
Justify:
a = _______
________________________
b = _______
________________________
c = _______
________________________
d = _______
________________________
e = _______
________________________
f = _______
________________________
g = _______
________________________
h = _______
________________________
k = _______
________________________
m = _______
________________________
p = _______
________________________
r = _______
________________________
s = _______
________________________
9. Complete the following flowchart, OR write a two-column proof.
10. Write a two-column proof.
Given: VW @ XY, WX @ YV
Prove: DWXV @ DYVX
11. Write a two-column proof.
Given: BD bisects ÐADC , DB ^ AC
Prove: DADC is isosceles
12. Write a two-column proof.
Given: See diagram
Prove: ST @ UQ
13. Complete the flow chart proof, OR write as a two-column proof.
14. Write a two-column proof.
Prove: AB CD
Complete the following two-column proofs.
*You may not need all the lines in the proof box*
15.
Given: See Diagram
Prove: FH @ JH
Statement
Reason
1.
2.
3.
4.
5.
6.
16. Given: AD @ CD , BD ^ CA
Prove: Ð1 @ Ð2
*You may not need all the lines in the proof box*
Statement
Reason
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Additional Study Suggestions:
☐ Create flashcards for key vocabulary and provide examples/diagrams in which they can be applied.
☐ Practice problems (especially proofs) until you can solve them on your own.
☐ Re-work problems from the notes, HW, textbook, workbook, & additional resources provided.
☐ Your teachers, tutors, peer tutors, and classmates are a great for extra help.
☐ Study at least a week before the test. Studying one or two days before is called procrastination!
Chapter 4: Congruent Triangles Review - KEY
Determine if the following triangles are congruent.
Diagram
Congruent
Triangles
Explanation
DLMN @ D NOP
(a)
or
SAS
Not congruent
DABE @ D CDE
(b)
or
SAS or ASA
Not congruent
DHIJ @ D HKJ
(c)
or
HL
Not congruent
DXYZ @ D ZWX
(d)
or
ASA
Not congruent
DRST @ D _______
(e)
or
SSA does not prove
congruency
Not congruent
DSTV @ D UTV
(f)
or
SSS
Not congruent
DITR @ D ERT
(g)
or
Not congruent
AAS
Draw the following triangles. If necessary, indicate on your drawing if sides or angles are
congruent.
Scalene Obtuse Triangle
Isosceles Acute Triangle
Regular Triangle
Solve for x and y. Justify your answer with definitions, postulates, and/or theorems.
1.
2.
3.
4.
5.
Answer:
6. Find the following angles. *Justify your answer with a
definition, postulate and/or theorem.
a = 112°
Linear Pair Post./Def. Supp.∠’s
b = 68°
Consecutive Interior ∠’s
c = 44
def. of ≅ ∠’s, ∠ add. post
/def. straight line
d = 44°
Triangle Sum Theorem,
or Alt. Int. ∠’s
e = 136°
Consec. Int. ∠’s OR Linear
Pr.Post./Def. Supp. ∠’s
f = 68°
VAT, ∆ Sum Thrm, Base
∠’s Thrm
g = 68°
Base ∠’s Theorem
h = 56°
VAT, ∆ Sum Thrm, Base
∠’s Thrm
k = 68°
Alt. Int. ∠’s
l = 56°
7. Find the following angles. *Justify your answer with a
definition, postulate and/or theorem.
Justify: ANSWERS VARY
∠ add. post /def. straight line
m = 124°
Consecutive Interior ∠’s
Answer:
Justify: ANSWERS VARY
a =37° Linear Pair Post./Def. Supp.∠’s
b = 143°
VAT or (same as above)
c = 37°
Alt. Int. ∠’s
d = 58°
∠ add. post./def. straight
line
e = 37°
VAT or (same as above)
f = 53°
∆ Sum Thrm
g = 48°
Base ∠’s Theorem
h = 84°
∆ Sum Thrm
k =96°
def. supp. ∠’s
m = 26°
∆ Sum Thrm
p = 69°
def. of ≅ ∠’s, AND
∆ Sum Thrm
8. Use the coordinates to determine if
.
Classify the triangles.
A(1, 3), B(4, 1), C(5, 3), D(3, -3), E(6, -5), F(7, -3).
r = 111°
def. supp. ∠’s
s = 69°
Consecutive Interior ∠’s
Scalene Acute ∆
9. Complete the following flowchart, OR write a two-column proof.
Statement
Reason
1. Given
2. Alternate Interior ∠’s Theorem
3. Given
1. SA @ NE
2. ∠3 ≅ ∠4
3. SE NA
4. ∠1 ≅ ∠2
5. SN SN
6. ∆ SEN ≅ ∆ NAS
7. SA @ NE
4. Alternate Interior Angle’s Theorem
5. Reflexive Property
6. ASA
7. CPCTC
10. Write a two-column proof.
Given:
Prove:
Statement
Reason
1.
1. Given
2. VX @ VX
3. ∆ WXV ≅ ∆ YVX
2. Reflexive Property
3. SSS
11. Write a two-column proof.
Given:
bisects
,
Prove: DADC is isosceles
Statement
1.
bisects
2. ∠1 ≅ ∠2
3. DB ^ AC
4. ∠3, ∠4 are Right Angles
5. ∠3 ≅ ∠4
6. DB @ DB
7. ∆ CDB ≅ ∆ ADB
8. CD @ AD
9. ∆ ADC is an isosceles
Reason
1. Given
2. Def. of Angle Bisector
3. Given
4. Perpendicular lines form 4 rights ∠’s theorem
5. Right Angles congruence theorem
6. Reflexive Property
7. ASA
8. CPCTC
9. Definition of Isosceles Triangle
12. Write a two-column proof.
Given: (See diagram)
Prove: ST @ UQ
Statement
1. QR @ RT (Side)
2. ∠QUR ≅ ∠RST (Angle)
3. ∠QRU ≅ ∠SRT (Angle)
4. ∆ QRU ≅ ∆ TRS
5. ST @ UQ
Reason
1. Given
2. Given
3. VAT
4. AAS
5.CPCTC
13. Complete the flow chart proof, OR write as a two-column proof.
Statement
1. I is the midpt. of CM
2. I is the midpt. of BL
3. CI @ IM (Side)
4. IL @ IB (Side)
5. ∠1 ≅ ∠2 (Angle)
6. ∆ LTC ≅ ∆ BIM
7. CL @ MB
Reason
1. Given
2. Given
3. Def. of midpt.
4. Def. of midpt.
5. VAT
6. SAS
7. CPCTC
14. Write a two-column proof.
Prove: AB CD
Statement
1. AB @ CD
2. AD @ BC
3. BD @ BD
4. ∆ ABD ≅ ∆ CDB
5. ∠ABD ≅ ∠CDB
6. AB CD
Reason
1. Given
2. Given
3. Reflexive Property
4. SSS
5. CPCTC
6. Alt. Interior Angles CONVERSE theorem
Complete the following two-column proofs.
*You may not need all the lines in the proof box*
15.
Given: (See Diagram)
Prove: FH @ JH
Statement
1.
2.
3.
4.
IJ @ GF
ÐG @ ÐI
ÐFHG @ ÐIHJ
DJIH @ DFGH
5. FH @ JH
Reason
Given
Given
Vertical angles theorem
AAS triangle congruence theorem
CPCTC
16. Given: AD @ CD , BD ^ CA
Prove: Ð1 @ Ð2
*You may not need all the lines in the proof box*
Statement
Reason
1. AD @ DC (Side)
Given
2. BD ^ AC
Given
3. ÐADB, ÐCDE are right
angles
Perpendicular lines form four right angles
Theorem
4. ÐADB @ ÐCDE (Angle)
Right angles congruence theorem
5. EB @ EB (Side)
Reflexive property segment congruence
6. DADB @ DCDB
SAS triangle congruence theorem
7. AB @ BC (Side)
CPCTC
8. BE @ BE (Side)
Reflexive property segment congruence
9. ÐABD @ ÐCBD (Angle)
CPCTC
10. DABE @ DCBE
SAS
11. Ð1 @ Ð2
CPCTC
Additional Study Suggestions:
☐ Create flashcards for key vocabulary and provide examples/diagrams in which they can be applied.
☐ Practice problems (especially proofs) until you can solve them on your own.
☐ Re-work problems from the notes, HW, textbook, workbook, & additional resources provided.
☐ Your teachers, tutors, peer tutors, and classmates are a great for extra help.
☐ Study at least a week before the test. Studying one or two days before is called procrastination!