Download PROVE: ∆ABC

Geometry
Proofs Practice
Name ______________________
Period ____ Date ___________
4.3-4.5 – Triangle Congruence Proofs (Part 2)
1. Complete the proof by providing the correct statement or reason.
GIVEN: AB ≅ CD , BC ≅ AD
PROVE: ∆ABC ≅ ∆CDA
Statements
1.
Reason
1. Given
2.
2.
3. ∆ABC ≅ ∆CDA
3.
Complete the proof.
2. GIVEN: WU  YV , XU  ZV , WX ≅ YZ
PROVE: ∆WXU ≅ ∆YZV
Statements
Reasons
1. WU  YV
1.
2. ∠UWX ≅ ∠VYZ
2.
3. XU  ZV
3.
4. ∠UXW ≅ ∠VZY
4.
5. WX ≅ YZ
5.
6. ∆WXU ≅ ∆YZV
6.
3. Complete the proof by providing the correct reason for each statement.
GIVEN: BE ≅ BC and ∠A ≅ ∠D
PROVE: ∆ABE ≅ ∆DBC
Statements
1.
Reason
1.
2.
2.
3.
3.
4. Complete the proof by providing the missing information.
GIVEN: AB  DC , ∠ ADB ≅ ∠ CBD
PROVE: ∆ABD ≅ ∆CDB
Statements
Reasons
5. Given: The coordinates of two triangles are ∆PVH : P(-6, 2), V(-1, 4), H(-2, -1)
and ∆NQR : N(2, -2), Q(4, -7), R(-1, -6).
(You will need to calculate the length of the sides by using the distance formula/Pythagorean Theorem.)
Prove: ∆PVH ≅ ∆NQR by using SSS
6. Given: The coordinates of two triangles are ∆PVH : P(-1, 6), V(-4, 4), H(0, -2)
and ∆NQR : N(5, -3), Q(3, -6), R(-3, -2).
(You will need to calculate length like in #5. You might need to calculate slope as well.)
Prove: ∆PVH ≅ ∆NQR by using HL
7. Complete the proof by providing the missing information.
GIVEN: B is the midpoint of AE .
B is the midpoint of CD .
PROVE: ∆ABD ≅ ∆EBC
Statements
Reasons
1. B is the midpoint of AE
1.
2.
2.
3. B is the midpoint of CD
3.
4.
4.
5.
5. Vertical Angles Congruence Theorem
6. ∆ABD ≅ ∆EBC
6.
Answer Bank for problems 1-4 and 7:
Given
Given
Given Given Given
Vertical Angles
Definition of midpoint
Congruence Theorem
Reflexive Property of
Alternate interior angles theorem
Congruence
Corresponding angles
SAS Postulate
SSS Postulate
postulate
ASA
AC ≅ CA
AB ≅ EB
BD ≅ DB
Postulate
Given
Given
Definition of midpoint
Corresponding angles postulate
ASA Postulate
AAS Postulate
DB ≅ CB
∠ABD ≅ ∠EBC
AB ≅ CD & BC ≅ AD
AB  DC & ∠ADB ≅ ∠CBD
BE ≅ BC ,
∠A ≅ ∠D
∠ ABD ≅ ∠ CDB
Reflexive Property of
Congruence
∆ABD ≅ ∆CDB
∆ABE ≅ ∆DBC
∠ABE ≅ ∠DBC
Answer bank for problems 5 and 6:
PH = 65
VH = 26
mPV =
PV = 29
mVH =
−3
2
NQ = 13
PH = 5
NQ = 29
QN ⊥ RQ
QR ≅ VH
2
3
NR = 5
3
2
PV = 13
mQN =
−2
3
m∠V = 90° PV ≅ NQ
PV ⊥ VH
∆PVH ≅ ∆NQR by HL Postulate
mRQ =
PH ≅ NR
∆PVH ≅ ∆NQR by SSS Postulate
QR = 26
VH = 52
NR = 65
QR = 52
VH ≅ QR
m∠Q = 90°
PH ≅ NR
PV ≅ NQ