Download Triangle Similarity: AA, SSS, SAS Quiz

Name: ________________________ Class: ___________________ Date: __________
Triangle Similarity: AA, SSS, SAS Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Explain why the triangles are similar and write a similarity statement.
____
∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
b. ∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆DBE by AA Similarity.
c. ∠A ≅ ∠BED and ∠C ≅ ∠BDE by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆EBD by AA Similarity.
d. ∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆EBD by AA Similarity.
2. Verify that ∆PQR ∼ ∆SQT .
a.
a.
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QS
QT 3
=
=
QP QR 5
∆PQR ∼ ∆SQT by SAS Similarity.
b.
∠P ≅ ∠QST and ∠R ≅ ∠QTS by the Corresponding Angles Postulate.
∆PQR ∼ ∆SQT by AA Similarity.
c.
∠P ≅ ∠QTS and ∠R ≅ ∠QST by the Alternate Interior Angles Theorem.
∆PQR ∼ ∆SQT by AA Similarity.
d.
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QT 2
PS
=
=
QP QR 5
∆PQR ∼ ∆SQT by SAS Similarity.
1
ID: A
Name: ________________________
____
ID: A
3. Explain why ∆ABC ∼ ∆DBE and then find BC.
a.
AC Ä DE by the Converse of the Corresponding Angles Postulate.
∠A ≅ ∠BDE by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 42 .
b.
AC Ä DE by the Converse of the Alternate Interior Angles Theorem.
∠A ≅ ∠BDE by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 14 .
c.
∠B ≅ ∠B by the Reflexive Property of Congruence.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 14 .
d.
∠A ≅ ∠BDE , ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 42 .
2
ID: A
Triangle Similarity: AA, SSS, SAS Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
Since AC Ä DE , ∠A ≅ ∠BDE , and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
Therefore ∆ABC ∼ ∆DBE by AA Similarity.
Feedback
A
B
C
D
Correct!
Are angles A, BED and angles C, BDE pairs of alternate interior angles?
Are angles A, BED and angles C, BDE pairs of alternate interior angles?
List the corresponding vertices in the same order when writing a similarity statement.
PTS: 1
DIF: Average
REF: 1b82c312-4683-11df-9c7d-001185f0d2ea
OBJ: 7-3.1 Using the AA Similarity Postulate
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
STA: NY.NYLES.MTH.05.GEO.G.G.44
LOC: MTH.C.11.08.03.03.002
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
KEY: similar triangles | correspondence | AA similarity
DOK: DOK 2
2. ANS: A
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QS
6
3 QT
9
3
=
= ,
=
=
QP 10 5 QR 15 5
Therefore ∆ABC ∼ ∆DBE by SAS Similarity.
Feedback
A
B
C
D
Correct!
Is it given that segment PR is parallel to ST?
Is it given that segment PR is parallel to ST? Are the angle pairs in this choice alternate
interior angles?
Is segment PS a side of one of the triangles? Are the ratios equal?
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1b82ea22-4683-11df-9c7d-001185f0d2ea
7-3.2 Verifying Triangle Similarity
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.44 | NY.NYLES.MTH.05.GEO.G.G.45
MTH.C.11.08.03.03.007
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
similar triangles | SAS similarity
DOK: DOK 2
1
ID: A
3. ANS: A
Step 1 Prove triangles are similar.
As shown ∠C ≅ ∠BED, so AC Ä DE by the Converse of the Corresponding Angles Postulate.
∠A ≅ ∠BDE by the Corresponding Angles Postulate.
Therefore ∆ABC ∼ ∆DBE by AA Similarity.
Step 2 Find BC.
DE BE
=
AC BC
32 28
=
48 BC
32(BC) = 28 ⋅ 48
32(BC) = 1344
BC = 42
Corresponding sides are proportional.
Substitute 32 for DE, 48 for AC, and 28 for BE.
Cross Products Property
Simplify.
Divide both sides by 32.
Feedback
A
B
C
D
Correct!
Are angles C and BED and angles A and BDE pairs of alternate interior angles? Can BC
equal 14 if BE equals 28?
You found the value of EC, not BC.
It is given that angles C and BED are congruent. You are also missing one step before
concluding that angles A and BDE are congruent.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: 1b85256e-4683-11df-9c7d-001185f0d2ea
7-3.3 Finding Lengths in Similar Triangles
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.44
LOC: MTH.C.11.08.03.03.002
7-3 Triangle Similarity: AA, SSS, and SAS
similar triangles | side length | AA similarity
DOK: DOK 2
2
Name: ________________________ Class: ___________________ Date: __________
Triangle Similarity: AA, SSS, SAS Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Explain why the triangles are similar and write a similarity statement.
____
∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆EBD by AA Similarity.
b. ∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
c. ∠A ≅ ∠BED and ∠C ≅ ∠BDE by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆EBD by AA Similarity.
d. ∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆DBE by AA Similarity.
2. Verify that ∆PQR ∼ ∆SQT .
a.
a.
∠P ≅ ∠QTS and ∠R ≅ ∠QST by the Alternate Interior Angles Theorem.
∆PQR ∼ ∆SQT by AA Similarity.
b.
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QS QT 3
=
=
QP QR 5
∆PQR ∼ ∆SQT by SAS Similarity.
c.
∠P ≅ ∠QST and ∠R ≅ ∠QTS by the Corresponding Angles Postulate.
∆PQR ∼ ∆SQT by AA Similarity.
d.
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QT 2
PS
=
=
QP QR 5
∆PQR ∼ ∆SQT by SAS Similarity.
1
ID: B
Name: ________________________
____
ID: B
3. Explain why ∆ABC ∼ ∆DBE and then find BC.
a.
AC Ä DE by the Converse of the Corresponding Angles Postulate.
∠A ≅ ∠BDE by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 42 .
b.
∠B ≅ ∠B by the Reflexive Property of Congruence.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 14 .
c.
AC Ä DE by the Converse of the Alternate Interior Angles Theorem.
∠A ≅ ∠BDE by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 14 .
d.
∠A ≅ ∠BDE , ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 42 .
2
ID: B
Triangle Similarity: AA, SSS, SAS Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: B
Since AC Ä DE , ∠A ≅ ∠BDE , and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
Therefore ∆ABC ∼ ∆DBE by AA Similarity.
Feedback
A
B
C
D
List the corresponding vertices in the same order when writing a similarity statement.
Correct!
Are angles A, BED and angles C, BDE pairs of alternate interior angles?
Are angles A, BED and angles C, BDE pairs of alternate interior angles?
PTS: 1
DIF: Average
REF: 1b82c312-4683-11df-9c7d-001185f0d2ea
OBJ: 7-3.1 Using the AA Similarity Postulate
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
STA: NY.NYLES.MTH.05.GEO.G.G.44
LOC: MTH.C.11.08.03.03.002
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
KEY: similar triangles | correspondence | AA similarity
DOK: DOK 2
2. ANS: B
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QS
6
3 QT
9
3
=
= ,
=
=
QP 10 5 QR 15 5
Therefore ∆ABC ∼ ∆DBE by SAS Similarity.
Feedback
A
B
C
D
Is it given that segment PR is parallel to ST? Are the angle pairs in this choice alternate
interior angles?
Correct!
Is it given that segment PR is parallel to ST?
Is segment PS a side of one of the triangles? Are the ratios equal?
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1b82ea22-4683-11df-9c7d-001185f0d2ea
7-3.2 Verifying Triangle Similarity
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.44 | NY.NYLES.MTH.05.GEO.G.G.45
MTH.C.11.08.03.03.007
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
similar triangles | SAS similarity
DOK: DOK 2
1
ID: B
3. ANS: A
Step 1 Prove triangles are similar.
As shown ∠C ≅ ∠BED, so AC Ä DE by the Converse of the Corresponding Angles Postulate.
∠A ≅ ∠BDE by the Corresponding Angles Postulate.
Therefore ∆ABC ∼ ∆DBE by AA Similarity.
Step 2 Find BC.
DE BE
=
AC BC
32 28
=
48 BC
32(BC) = 28 ⋅ 48
32(BC) = 1344
BC = 42
Corresponding sides are proportional.
Substitute 32 for DE, 48 for AC, and 28 for BE.
Cross Products Property
Simplify.
Divide both sides by 32.
Feedback
A
B
C
D
Correct!
You found the value of EC, not BC.
Are angles C and BED and angles A and BDE pairs of alternate interior angles? Can BC
equal 14 if BE equals 28?
It is given that angles C and BED are congruent. You are also missing one step before
concluding that angles A and BDE are congruent.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: 1b85256e-4683-11df-9c7d-001185f0d2ea
7-3.3 Finding Lengths in Similar Triangles
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.44
LOC: MTH.C.11.08.03.03.002
7-3 Triangle Similarity: AA, SSS, and SAS
similar triangles | side length | AA similarity
DOK: DOK 2
2
Name: ________________________ Class: ___________________ Date: __________
Triangle Similarity: AA, SSS, SAS Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Explain why the triangles are similar and write a similarity statement.
____
∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆DBE by AA Similarity.
b. ∠A ≅ ∠BED and ∠C ≅ ∠BDE by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆EBD by AA Similarity.
c. ∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆EBD by AA Similarity.
d. ∠A ≅ ∠BDE and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
2. Verify that ∆PQR ∼ ∆SQT .
a.
a.
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QT 2
PS
=
=
QP QR 5
∆PQR ∼ ∆SQT by SAS Similarity.
b.
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QS QT 3
=
=
QP QR 5
∆PQR ∼ ∆SQT by SAS Similarity.
c.
∠P ≅ ∠QTS and ∠R ≅ ∠QST by the Alternate Interior Angles Theorem.
∆PQR ∼ ∆SQT by AA Similarity.
d.
∠P ≅ ∠QST and ∠R ≅ ∠QTS by the Corresponding Angles Postulate.
∆PQR ∼ ∆SQT by AA Similarity.
1
ID: C
Name: ________________________
____
ID: C
3. Explain why ∆ABC ∼ ∆DBE and then find BC.
a.
AC Ä DE by the Converse of the Alternate Interior Angles Theorem.
∠A ≅ ∠BDE by the Alternate Interior Angles Theorem.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 14 .
b.
∠A ≅ ∠BDE , ∠C ≅ ∠BED by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 42 .
c.
AC Ä DE by the Converse of the Corresponding Angles Postulate.
∠A ≅ ∠BDE by the Corresponding Angles Postulate.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 42 .
d.
∠B ≅ ∠B by the Reflexive Property of Congruence.
∆ABC ∼ ∆DBE by AA Similarity.
Corresponding sides are proportional, so BC = 14 .
2
ID: C
Triangle Similarity: AA, SSS, SAS Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: D
Since AC Ä DE , ∠A ≅ ∠BDE , and ∠C ≅ ∠BED by the Corresponding Angles Postulate.
Therefore ∆ABC ∼ ∆DBE by AA Similarity.
Feedback
A
B
C
D
Are angles A, BED and angles C, BDE pairs of alternate interior angles?
Are angles A, BED and angles C, BDE pairs of alternate interior angles?
List the corresponding vertices in the same order when writing a similarity statement.
Correct!
PTS: 1
DIF: Average
REF: 1b82c312-4683-11df-9c7d-001185f0d2ea
OBJ: 7-3.1 Using the AA Similarity Postulate
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
STA: NY.NYLES.MTH.05.GEO.G.G.44
LOC: MTH.C.11.08.03.03.002
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
KEY: similar triangles | correspondence | AA similarity
DOK: DOK 2
2. ANS: B
∠Q ≅ ∠Q by the Reflexive Property of Congruence.
QS
6
3 QT
9
3
=
= ,
=
=
QP 10 5 QR 15 5
Therefore ∆ABC ∼ ∆DBE by SAS Similarity.
Feedback
A
B
C
D
Is segment PS a side of one of the triangles? Are the ratios equal?
Correct!
Is it given that segment PR is parallel to ST? Are the angle pairs in this choice alternate
interior angles?
Is it given that segment PR is parallel to ST?
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1b82ea22-4683-11df-9c7d-001185f0d2ea
7-3.2 Verifying Triangle Similarity
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.44 | NY.NYLES.MTH.05.GEO.G.G.45
MTH.C.11.08.03.03.007
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
similar triangles | SAS similarity
DOK: DOK 2
1
ID: C
3. ANS: C
Step 1 Prove triangles are similar.
As shown ∠C ≅ ∠BED, so AC Ä DE by the Converse of the Corresponding Angles Postulate.
∠A ≅ ∠BDE by the Corresponding Angles Postulate.
Therefore ∆ABC ∼ ∆DBE by AA Similarity.
Step 2 Find BC.
DE BE
=
AC BC
32 28
=
48 BC
32(BC) = 28 ⋅ 48
32(BC) = 1344
BC = 42
Corresponding sides are proportional.
Substitute 32 for DE, 48 for AC, and 28 for BE.
Cross Products Property
Simplify.
Divide both sides by 32.
Feedback
A
B
C
D
Are angles C and BED and angles A and BDE pairs of alternate interior angles? Can BC
equal 14 if BE equals 28?
It is given that angles C and BED are congruent. You are also missing one step before
concluding that angles A and BDE are congruent.
Correct!
You found the value of EC, not BC.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: 1b85256e-4683-11df-9c7d-001185f0d2ea
7-3.3 Finding Lengths in Similar Triangles
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.44
LOC: MTH.C.11.08.03.03.002
7-3 Triangle Similarity: AA, SSS, and SAS
similar triangles | side length | AA similarity
DOK: DOK 2
2