Download Practice C 4.4 CRB

Name ———————————————————————
Practice C
LESSON
4.4
LESSON 4.4
Date ————————————
For use with pages 250–257
Decide whether enough information is given to prove that the
triangles are congruent. If there is enough information, state the
congruence postulate or theorem you would use.
1. n ABC, n FEC
2. n GHI, n JKL
B
J
H
A
I
C
L
E
K
F
G
3. n MNO, n PQR
4. n STX, n VUW
P
T
U
X
W
O
N
S
R
V
State the third congruence that must be given to prove that n ABC > n FED
using the indicated postulate or theorem.
} } } }
5. GIVEN: BC ù ED, AC ù FD,
? ù ?
Use the SAS Congruence Postulate.
} } } }
6. GIVEN: AB ù FE, AC ù FD, ? ù ?
Use the SSS Congruence Postulate.
} }
7. GIVEN: BC ù ED, ∠ B is a right angle and
∠ B ù ∠ E, ? ù ?
Use the HL Congruence Theorem.
}
B
A
}
}
D
8. Suppose P is the midpoint of OQ in n OQS. If SP ⊥ OQ, explain why
n SPO ù n SPQ.
254
Geometry
Chapter 4 Resource Book
E
C
F
Copyright © Holt McDougal. All rights reserved.
M
Name ———————————————————————
Practice C
LESSON
4.4
For use with pages 250–257
continued
} }
} }
S
R
LESSON 4.4
9. Proof Complete the proof.
}
Date ————————————
}
GIVEN: QS ù PR, PS ⊥ RS, QR ⊥ RS
PROVE: n PRS ù n QSR
P
Statements
} }
1. QS ù PR
} } } }
2. PS ⊥ RS, QR ⊥ RS
Reasons
3. ∠ S and ∠ R are right angles.
3.
4.
4. Definition of a right triangle
1. Given
2. Given
?
?
} }
5. RS ù SR
5.
?
6. n PRS ù n QSR
6.
?
10. Proof Complete the proof.
O
} } } }
GIVEN: OM ⊥ LN, ML > MN
PROVE: n OML ù n OMN
Copyright © Holt McDougal. All rights reserved.
L
M
N
Reasons
Statements
} }
1. OM ⊥ LN
1. Given
2.
2. If 2 angles are ⊥, then they form 4 right ?.
3.
?
3. Right Angle Congruence Theorem
?
}
}
4. ML > MN
} }
5. OM > OM
4.
?
5.
?
6. n OML ù n OMN
6.
?
Geometry
Chapter 4 Resource Book
255
Lesson 4.3, continued
Statements
} }
6. AF > EC
7. n AFB > n CEB
4.
Copyright © Holt McDougal. All rights reserved.
Statements
1. n ZWV > n YXV
} }
2. ZW > YX
}
}
VZ > VY
} }
WV > XV
3. WV 1 VY 5 WY
XV 1 VZ 5 XZ
4. WV 5 XV; VZ 5 VY
Reasons
1. Given
2. Definition of
congruent triangles
3. Segment Addition
Postulate
4. Definition of
Congruent Segments
5. XV 1 VZ 5 WY
5. Substitution property
of equality
6. WY 5 XZ
6. Substitution property
of equality
} }
7. Definition of
7. WY > XZ
congruent segments
} }
8. Reflexive prop. of
8. ZY > ZY
congruence
9. n ZWY > n YXZ
9. SSS Congruence
Postulate
5. The diagram shows two equilateral triangles,
n ABC and n DEF. If one side of n ABC is
congruent to one side of n DEF, such as
} }
AB > DE, then you know that the triangles are
congruent because equilateral triangles have three
E
B
congruent sides.
A
C
D
F
6. J(3, 9), K(7, 8)
Lesson 4.4
1. ∠ ABC 2. ∠ BCD 3. ∠ ABD 4. ∠ BDA
5. ∠ DAB 6. ∠ CDB 7. not enough 8. enough
9. not enough 10. Yes, SAS Congruence
Postulate 11. Yes, HL Congruence Theorem
} }
12. not enough 13. RM ù FB 14. ∠ J ù ∠ D
} }
} } } }
15. JM ù DB or JR ù DF 16. Given; AB ù BE;
} }
Given; CB ù BD; Vertical Angles Theorem;
SAS Congruence Postulate 17. Given; Alternate
Interior Angles Theorem; Given; Reflexive
Property of Congruence; SAS Congruence
Postulate
Practice Level C
1. not enough 2. enough; HL 3. not enough
} }
4. enough; SAS 5. ∠ BCA; ∠ EDF 6. BC; ED
} }
7. AC; FD 8. They are congruent by SAS.
9. Definition of perpendicular lines; n PRS and
n QSR are right triangles; Reflexive Property of
Congruence; HL Congruence Theorem
10. ∠ OML and ∠ OMN are right angles;
∠ OML ù ∠ OMN; Given; Reflexive Property of
Congruence; SAS Congruence Postulate
Review for Mastery
1. Yes; You are given that two sides and the
included angle of one triangle are congruent
to two sides and the included angle of another
triangle.
2. Yes; ∠ JKN and ∠ MKL are congruent because
they are vertical angles. So you have two sides
and the included angle of one triangle that are
congruent to two sides and the included angle of
another triangle. 3. No; You have two sides in
nWXY that are congruent to two sides in n ZXY,
but the angle in n ZXY is not the included angle.
4.
Practice Level A
1. ∠ GHI
Practice Level B
ANSWERS
Reasons
6. Definition of
congruent segments
7. SSS Congruence
Postulate
2. ∠ HIG 3. ∠ IGH
4. ∠ GIJ
5. ∠ JGI 6. ∠ IJG 7. enough 8. not enough
9. enough 10. not enough 11. enough
} }
} }
12. not enough 13. AB; DE 14. AC; DF
} }
15. BC; EF 16. Two sides and the included
angle of one ramp need to be congruent to the
corresponding sides and angle of the second ramp;
the two ramps need to be right triangles with
congruent hypotenuses and one pair of congruent
corresponding legs.
Statements
} }
H 1. AB > DB
} }
2. BC ⊥ AD
3. ∠ ACB and ∠ DCB
are right angles.
4. n ABC and n DCB
are right triangles.
} }
L 5. BC > BC
6. n ABC > n DBC
Reasons
1. Given
2. Given
3. Def. of ⊥ lines
4. Def. of a right
triangle
5. Reflexive Property
of Congruence
6. HL Congruence
Theorem
Geometry
Chapter 4 Resource Book
A45