Which of the following are given statements?

B C ‾ ≅ E F ‾ \overline{BC}\cong\overline{EF} B C ≅ E F

A C ‾ ≅ D F ‾ \overline{AC}\cong\overline{DF} A C ≅ D F

A B ‾ ≅ D E ‾ \overline{AB}\cong\overline{DE} A B ≅ D E

∠ A ≅ ∠ D \angle A\cong\angle D ∠ A ≅ ∠ D

Identify the missing pair of congruent pieces needed to prove the triangles congruent using the named theorem.

< B ≅ < Y <B\ \cong\ <Y < B ≅ < Y

A C ≅ X Z AC\ \cong\ XZ A C ≅ X Z

< C ≅ < Y <C\ \cong<Y < C ≅ < Y

B C ≅ Y Z BC\ \cong\ YZ B C ≅ Y Z

Identify the missing pair of congruent pieces needed to prove the triangles congruent using the named theorem.

A B ≅ X Y AB\ \cong\ XY A B ≅ X Y

B C ≅ Y Z BC\ \cong\ YZ B C ≅ Y Z

< C ≅ < Z <C\ \cong\ <Z < C ≅ < Z

A C ≅ X Z AC\ \cong\ XZ A C ≅ X Z

Identify the missing pair of congruent pieces needed to prove the triangles congruent using the named theorem.

< A ≅ < X <A\ \cong\ <X < A ≅ < X

< C ≅ < Z <C\ \cong\ <Z < C ≅ < Z

A C ≅ X Z AC\ \cong\ XZ A C ≅ X Z

A B ≅ X Y AB\ \cong\ XY A B ≅ X Y

Identify the missing pair of congruent pieces needed to prove the triangles congruent using the named theorem.

A B ≅ X Y AB\ \cong\ XY A B ≅ X Y

B C ≅ Y Z BC\ \cong\ YZ B C ≅ Y Z

< C ≅ < Z <C\ \cong\ <Z < C ≅ < Z

A C ≅ X Z AC\ \cong\ XZ A C ≅ X Z

Identify the missing pair of congruent pieces needed to prove the triangles congruent using HL theorem. MORE than one correct answer!

< 1 & < 2 a r e r i g h t a n g l e s <1\ \&\ <2\ are\ \ right\ \ angles < 1 & < 2 a r e r i g h t a n g l e s

< C & < K a r e r i g h t a n g l e s <C\ \&\ <K\ are\ \ right\ \ angles < C & < K a r e r i g h t a n g l e s

< C E A & < K A E a r e r i g h t a n g l e s <CEA\ \&\ <KAE\ are\ \ right\ \ angles < C E A & < K A E a r e r i g h t a n g l e s

A C ≅ E K AC\ \cong\ EK A C ≅ E K

Identify the missing pair of congruent pieces needed to prove the triangles congruent using the named theorem.

< D ≅ < M <D\ \cong\ <M < D ≅ < M

< E ≅ < N <E\cong\ <N < E ≅ < N

D E ≅ M N DE\cong\ MN D E ≅ M N

E F ≅ N O EF\ \cong\ NO E F ≅ N O

Identify the missing pair of congruent pieces needed to prove the triangles congruent using the named theorem.

< D ≅ < M <D\ \cong\ <M < D ≅ < M

< E ≅ < N <E\cong\ <N < E ≅ < N

D F ≅ M O DF\cong\ MO D F ≅ M O

E F ≅ N O EF\ \cong\ NO E F ≅ N O

State what additional information is required to prove the triangles are congruent by postulate ASA.

D E ‾ ≅ J K ‾ \overline{DE}\cong\overline{JK} D E ≅ J K

∠ F ≅ ∠ L \angle F\cong\angle L ∠ F ≅ ∠ L

D F ‾ ≅ J L ‾ \overline{DF}\cong\overline{JL} D F ≅ J L

F E ‾ ≅ L K ‾ \overline{FE}\cong\overline{LK} F E ≅ L K

We are given that A B ‾ ≅ B C ‾ ; \overline{AB}\cong\overline{BC}; A B ≅ B C ; therefore, ∠ A ≅ ∠ C \angle A\cong\angle C ∠ A ≅ ∠ C by the

Alternate Exterior Angles Theorem

Alternate Interior Angles Theorem

Because of the Definition of a Midpoint, we know that

A E ‾ ≅ C E ‾ \overline{AE}\cong\overline{CE} A E ≅ C E

A E ‾ ≅ B E ‾ \overline{AE}\cong\overline{BE} A E ≅ B E

A E ‾ ≅ B C ‾ \overline{AE}\cong\overline{BC} A E ≅ B C

A E ‾ ≅ A E ‾ \overline{AE}\cong\overline{AE} A E ≅ A E

We are given that W Z ‾ ∥ X Y ‾ , W X ‾ ∥ Z Y ‾ ; \overline{WZ}\parallel\overline{XY},\ \overline{WX}\parallel\overline{ZY}; W Z ∥ X Y , W X ∥ Z Y ; therefore __________________ by Reflexive Property of Congruence.

X Z ‾ ≅ X Z ‾ \overline{XZ}\cong\overline{XZ} X Z ≅ X Z

W Z ‾ ≅ W Z ‾ \overline{WZ}\cong\overline{WZ} W Z ≅ W Z

X Y ‾ ≅ X Y ‾ \overline{XY}\cong\overline{XY} X Y ≅ X Y

W X ‾ ≅ W X ‾ \overline{WX}\cong\overline{WX} W X ≅ W X

Bayleigh argued that, in the diagram, ∠ O N P ≅ ∠ Q P N \angle ONP\cong\angle QPN ∠ O N P ≅ ∠ Q P N because of SSS and CPCTC. Which statement is true?

Bayleigh does not have enough information to prove the triangles congruent by SSS.

Bayleigh's argument is correct.

Bayleigh should have used a reason other than CPCTC to make her final conclusion.

Bayleigh should have used SAS, not SSS to prove the triangles are congruent.

Which set of information is NOT enough to prove that ∆ A B C ∆ABC ∆ A B C is congruent to ∆ D E F ∆DEF ∆ D E F .

∠ A ≅ ∠ D ∠A≅∠D ∠ A ≅ ∠ D A C ‾ ≅ D F ‾ \overline{AC}≅\overline{DF} A C ≅ D F B C ‾ ≅ E F ‾ \overline{BC}≅\overline{EF} B C ≅ E F

∠ A ≅ ∠ D ∠A≅∠D ∠ A ≅ ∠ D ∠ C ≅ ∠ F ∠C≅∠F ∠ C ≅ ∠ F B C ‾ ≅ E F ‾ \overline{BC}≅\overline{EF} B C ≅ E F

∠ A ≅ ∠ D ∠A≅∠D ∠ A ≅ ∠ D ∠ C ≅ ∠ F ∠C≅∠F ∠ C ≅ ∠ F A C ‾ ≅ D F ‾ \overline{AC}≅\overline{DF} A C ≅ D F

A B ‾ ≅ D E ‾ \overline{AB}≅\overline{DE} A B ≅ D E B C ‾ ≅ E F ‾ \overline{BC}≅\overline{EF} B C ≅ E F ∠ B ≅ ∠ E ∠B≅∠E ∠ B ≅ ∠ E

Determine whether the triangles are congruent by SSS, SAS, ASA, AAS, HL or not congruent. If they are congruent, write a congruency statement.

Yes \Delta CAB\cong\Delta FED Δ C A B ≅ Δ F E D by SAS

Yes Δ C A B ≅ Δ F E D \Delta CAB\cong\Delta FED Δ C A B ≅ Δ F E D by SSS

Yes \Delta CAB\cong\Delta FED Δ C A B ≅ Δ F E D by SSS

Yes Δ A B C ≅ Δ F E D \Delta ABC\cong\Delta FED Δ A B C ≅ Δ F E D by SAS

Determine whether the triangles are congruent or not. If yes, find the correct congruency statement.

Yes Δ S R T ≅ Δ W V U \Delta SRT\cong\Delta WVU Δ S R T ≅ Δ W V U by SAS

Yes Δ R T S ≅ Δ W V U \Delta RTS\cong\Delta WVU Δ R T S ≅ Δ W V U by HL

Yes Δ S R T ≅ Δ W V U \Delta SRT\cong\Delta WVU Δ S R T ≅ Δ W V U by ASA

Yes \Delta RTS\cong\Delta WVU Δ R T S ≅ Δ W V U by SAS

Determine whether the triangles are congruent by SSS, SAS, ASA, AAS, HL, or not congruent. If yes, find the correct congruency statement below.

Yes, \Delta WXY\cong\Delta AZY Δ W X Y ≅ Δ A Z Y by AAS

Yes, Δ W X Y ≅ Δ A Z Y \Delta WXY\cong\Delta AZY Δ W X Y ≅ Δ A Z Y by ASA

Yes, \Delta WXY\cong\Delta AZY Δ W X Y ≅ Δ A Z Y by SAS

Determine whether the triangles are congruent by SSS, SAS, ASA, AAS, HL, or not congruent. If yes, find the correct congruency statement below.

Yes, Δ Z B A ≅ Δ B Z C \Delta ZBA\cong\Delta BZC Δ Z B A ≅ Δ B Z C by SAS

Yes, \Delta ZBA\cong\Delta BZC Δ Z B A ≅ Δ B Z C by ASA

Yes, \Delta ZBA\cong\Delta BZC Δ Z B A ≅ Δ B Z C by AAS

Determine whether the triangles are congruent by SSS, SAS, ASA, AAS, HL, or not congruent. If yes, find the correct congruency statement below.

Yes, \Delta EDC\cong\Delta EBA Δ E D C ≅ Δ E B A by both SAS and SSS

Yes, \Delta EDC\cong\Delta EBA Δ E D C ≅ Δ E B A by SAS

Yes, \Delta EDC\cong\Delta EBA Δ E D C ≅ Δ E B A by SSS

cong triangles

Authored by Katherine Filano

Mathematics

9th - 12th Grade

CCSS covered

Used 2+ times

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79 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\overline{JK}\ \cong\ ?$

$\overline{KX}$

$\overline{JK}$

$\overline{XJ}$

$\overline{KI}$

Tags

CCSS.HSG.CO.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\overline{LK}\ \cong\ ?$

$\overline{JE}$

$\overline{JF}$

$\overline{EF}$

$\overline{KJ}$

Tags

CCSS.HSG.CO.B.7

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\overline{JK}\ \cong\ ?$

$\overline{KX}$

$\overline{JK}$

$\overline{XJ}$

$\overline{KI}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What statement should go into #4?

$\overline{LM}\cong\overline{OP}$

$N\ is\ the\ midpoint\ of\ \overline{MO}$

$\overline{MN}\cong\overline{ON}$

$\overline{LN}\cong\overline{PN}$

Tags

CCSS.HSG.SRT.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which segment is part of both triangles?

$\overline{PR}$

$\overline{QS}$

$\overline{PS}$

$\overline{QS}$

Tags

CCSS.HSG.SRT.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Do you need anything beyond the given statements to prove the triangles congruent?

Yes

Not Enough information

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

By your proof, what reason are the 2 triangles congruent?

SAS

ASA

SSS

AAS

Tags

CCSS.HSG.SRT.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which angles are vertical?

$\angle B\ and\ \angle E$

$\angle A\ and\ \angle D$

$\angle BCA\ and\ \angle ECD$

$\angle B,\ \angle D$

Tags

CCSS.7.G.B.5

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which piece is part of both triangles?

$\overline{BD}$

$\angle C$

$\overline{AD}$

$\overline{BC}$

Tags

CCSS.8.G.A.2

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cong triangles

JK‾ ≅ ?\overline{JK}\ \cong\ ?JK ≅ ?

LK‾ ≅ ?\overline{LK}\ \cong\ ?LK ≅ ?

JK‾ ≅ ?\overline{JK}\ \cong\ ?JK ≅ ?

What statement should go into #4?

Which segment is part of both triangles?

Do you need anything beyond the given statements to prove the triangles congruent?

By your proof, what reason are the 2 triangles congruent?

According to your proof, why are these two triangles congruent?

Which angles are vertical?

Which piece is part of both triangles?

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$\overline{JK}\ \cong\ ?$

$\overline{LK}\ \cong\ ?$

$\overline{JK}\ \cong\ ?$