Congruency Proofs

The figure shows two triangles sharing side AB, where x represents the length of AB. Create an inequality that shows all possible values for x.

• 1 < x < 15

• 2 < x < 24

• 2 < x < 15

• x > 0

Which statement could be used to prove l ∥ m and a ∥ b?

• ∠13 ≅ ∠16 and ∠14 ≅ ∠11

• ∠2 ≅ ∠11 and ∠2 ≅ ∠7

• ∠7 ≅ ∠13 and ∠6 and ∠1 are supplementary

• ∠9 and ∠11 are supplementary and ∠7 and ∠8 are supplementary

Tags

CCSS.8.G.A.5

Are any of these line segments parallel? Choose the pair that is parallel.

• DC and FE

• AB and DC

• AB and GH

• FE and GH

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Can we use SAS, AAS, ASA, or SSS to prove Triangle ABE congruent to Triangle DEC?

• SAS

• AAS

• ASA

• SSS

Tags

CCSS.HSG.SRT.B.5

Is E the midpoint of AD?

• Yes, because AE = ED and E lies on AD

• No, because AE ≠ ED

• No, because E is not on AD

• Cannot be determined

Tags

CCSS.HSG.GPE.B.6

Using the diagram with triangles ABE and DEC sharing point E on intersecting segments AD and BC, determine whether Triangle ABE is congruent to Triangle DEC by one of SAS, AAS, ASA, or SSS, and whether E is the midpoint of AD.

• Congruent by SAS; E is the midpoint of AD

• Congruent by ASA; E is the midpoint of AD

• Congruent by AAS; E is not the midpoint of AD

• Congruent by SSS; E is not the midpoint of AD

Tags

CCSS.HSG.SRT.B.5

Using the diagram with triangles ABE and DEC sharing point E on intersecting segments AD and BC, determine whether Triangle ABE is congruent to Triangle DEC by one of SAS, AAS, ASA, or SSS, and whether E is the midpoint of AD.

• Congruent by SAS; E is the midpoint of AD

• Congruent by ASA; E is the midpoint of AD

• Congruent by AAS; E is not the midpoint of AD

• Congruent by SSS; E is not the midpoint of AD

Tags

CCSS.HSG.SRT.B.5

Can we use SAS, AAS, ASA, or SSS to prove Triangle ABE congruent to Triangle DEC? Choose the valid postulate, or select None of these if no conclusion is supported by the diagram.

• SAS

• ASA

• AAS

• SSS

• None of these

Tags

CCSS.HSG.SRT.B.5

Can we use SAS, AAS, ASA, or SSS to prove Triangle ABE congruent to Triangle DEC? Choose the valid postulate, or select None of these if no conclusion is supported by the diagram.

• SAS

• ASA

• AAS

• SSS

• None of these

Tags

CCSS.HSG.SRT.B.5

Which congruence postulate (SAS, ASA, AAS, or SSS) can be used to prove Triangle PQR is congruent to Triangle STU? Select the correct postulate or choose None of these if congruence cannot be determined from the diagram.

• AAS

• SAS

• ASA

• None of these

• SSS

Tags

CCSS.HSG.SRT.B.5