be able to identify which triangles can be constructed by the methods: sss, sas, aas, asa, ssa, or...
DESCRIPTION
Name the two pair of alternate interior angles: ___________ & ___________ and ___________ & ___________ Name the vertical angles in the triangles: ___________& ___________ Name the side included by VPR and V :__________ You may use the study guide on the exam only if you have completed every problem. Name the pair of congruent angles created if GH bisectors QGR: _______________ & _________________ Name the pair of congruent angles created if GH bisectors QHR: _______________ & _________________ Name the angle included by QH and QG: __________ Name the pair of congruent segments created if W is the midpoint of OT: _______________ & _________________ Name the vertical angles in the triangles: ___________& ___________ Name the angle opposite BO: __________ Name the side opposite I:___________ p.3TRANSCRIPT
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Be able to identify which triangles can be constructed by the methods: SSS, SAS, AAS, ASA, SsA, or HL.
Be able to construct those triangles that can be constructed and identify the method.
1. Construct ABC with 2. Construct DEF with
AB = 3”, BC = 2” , CA = 3” DE = 3”, mE=86, EF = 2”
3. Construct GHI with 4. Construct JKL with
mG=35, GH = 3”, HI = 2” mL=59, KL = 2”, JK = 3”
Your exam will be on _________________You may use the study guide on the exam only if you have completed every problem.
Constructing & Proving CongruentTriangles Study Guide
Name:____________________
p.1
Hint: SSS Hint: SAS
Hint: ASS Hint: SsA
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5. Construct MNO with 6. Construct PRQ with
mM=35, MN = 3”, mN=86, PR = 3”, mR=86, mQ=59
7. Construct STU with 8. Construct VYX with
mS=35, mT=86, mU=59 mV=90, XV = 4”, YX = 5”
p.2
Hint: ASA Hint: AAS
Hint: AAA Hint: SsA or HL
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Name the two pair of alternate interior angles:
___________ & ___________ and ___________ & ___________
Name the vertical angles in the triangles: ___________& ___________
Name the side included by VPR and V :__________
You may use the study guide on the exam only if you have completed every problem.
Name the pair of congruent angles created if GH bisectors QGR:
_______________ & _________________
Name the pair of congruent angles created if GH bisectors QHR:
_______________ & _________________
Name the angle included by QH and QG: __________
Name the pair of congruent segments created if W is the midpoint of OT:
_______________ & _________________
Name the vertical angles in the triangles: ___________& ___________
Name the angle opposite BO: __________
Name the side opposite I:___________
p.3
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Name the right angles formed BE AD:
_______________ & _________________
Name the right angles formed AE CD:
_______________ & _________________
Name the part in the overlapping triangles that is congruent to itself by Reflexive Property. _______________
B
C
A
D
E
Name the pair of congruent segments created if N is the midpoint of JK:
_______________ & _________________
Name the part in both triangles that is congruent to itself by Reflexive Property. _______________
Name the hypotenuse: ______________________________
Name the legs: ____________________________________
Which pair of triangles can be assumed congruent by SsA? ________
A. B.
Write the congruence statement for those triangles. ______________________________________
p.4
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You may use the study guide on the exam only if you have completed every problem.
Copy the SSS congruence theorem:
Find and copy or complete this proof:
Copy the SAS congruence theorem
Find and copy or complete this proof:
Given: XA = YA and XC = YC
Prove: XAC YACA
Y
C
X
p.5
Hint: to prove ∆XAC∆YAC apply reflexive property & SSSTo XAC YAC apply CPCF
Hint: to prove ∆JUE∆ILU apply vertical angles & SASTo JE LI apply CPCF
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You may use the study guide on the exam only if you have completed every problem.
Copy the ASA congruence theorem:
Find and copy or complete this proof:
Copy the AAS congruence theorem:
Find and copy or complete this proof:
Given: mADB = mCDB mABD = mCBD
Prove: AB = CB B C
A
D
p.6
Hint: to prove ∆ABD∆CBD apply reflexive property & ASATo AB =CB apply CPCF
Hint: to prove ∆PRS∆TQR apply reflexive property & AAS
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Given: ON > OG, ON FE OG GE
To prove: GNO GFE
You may use the study guide on the exam only if you have completed every problem.
Copy the SsA congruence theorem:
Find and copy or complete this proof:
Copy the HL congruence theorem:
Find and copy or complete this proof: Given: VXWY and WZ = VY XZ = XY Prove: W V
W Y
V
X
Z
p.7
Hint: to prove ∆GNO∆GFE vertical angles & SsA
Hint: to prove ∆WXZ∆VXY apply HL or SsATo WV apply CPCF