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

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

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

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

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

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

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