AnswersAZ-Common Core Geometry AIntroduction to Transformations

Triangle Congruence: SAS Answers

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1
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Which rigid transformations would map ΔJKL onto ΔPQR? Select the three correct answers.

A
a reflection only
B
a rotation only
C
a rotation and a reflection
D
a translation and a reflection
E
a translation only
2
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translatereflectrotate

A
translate
B
reflect
C
rotate
3

DCE and DBFDFE and DEFFDC and EDB

A
DCE and DBF
B
DFE and DEF
C
FDC and EDB
111584

XYZ

A
X
B
Y
C
Z
111588

Complete the missing parts of the paragraph proof.

Answers:
We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent to segment by the definition of isosceles triangle. Since these seg:it is given
We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent to segment by the definition of isosceles triangle. Since these seg:DE
We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent to segment by the definition of isosceles triangle. Since these seg:DFE and DEF
We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent to segment by the definition of isosceles triangle. Since these seg:DFB and DEC
111591

DFB and DECECD and DBCFDC and EDB

A
DFB and DEC
B
ECD and DBC
C
FDC and EDB
111592

To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed?

A
∠DEF ≅ ∠ DGF
B
∠DFE ≅ ∠ DFG
C
DE ≅ DG
D
DG ≅ GF
111593

What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

A
UV = 14 ft and m∠TUV = 45°
B
TU = 26 ft
C
m∠STU = 37° and m∠VTU = 37°
D
ST = 20 ft, UV = 14 ft, and m∠UST = 98°
E
m∠UST = 98° and m ∠TUV = 45°
111594

Can ΔTSR and ΔQRS be proven congruent by SAS?

A
yes, because along with the given information on the diagram, SR ≅ RS by the reflexive property
B
yes, because a reflection will map ΔTSR onto ΔQRS
C
yes, because P appears to be the midpoint of SQ and TR
D
no, because not enough is information given to prove the triangles congruent by SAS
111595

definition of midpointdefinition of segment bisectorreflexive property

A
definition of midpoint
B
definition of segment bisector
C
reflexive property
111596

Tamir is working to prove the triangles congruent using SAS. After stating the given information, he states that TQ ≅ QS by the definition of segment bisector. Now he wants to state that ∠RQT ≅ ∠PQS. Which reason should he use?

A
alternate interior angles theorem
B
corresponding angles theorem
C
linear pair postulate
D
vertical angles theorem
111597

Consider ΔWXY and ΔBCD with ∠X ≅∠C, WX ≅ BC, and WY ≅ BD.Can it be concluded that ΔWXY ≅ ΔBCD by SAS? Why or why not?

A
no, because the third corresponding sides must also be given as congruent
B
no, because the corresponding congruent angles listed are not the included angles
C
no, because all corresponding angles must be given as congruent
D
yes, because two corresponding sides and a corresponding angle are congruent
111598

angles BCA and DCA form a linear pairangle BCA is congruent to angle DCAsegment AC is perpendicular to segment BD

A
angles BCA and DCA form a linear pair
B
angle BCA is congruent to angle DCA
C
segment AC is perpendicular to segment BD
111599

DBDCDE

A
DB
B
DC
C
DE
111600

of the definition of isosceles triangleit is givenreflexive property

A
of the definition of isosceles triangle
B
it is given
C
reflexive property

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