Geometry G3 HW 3
Due 10/18
Proofs
1. Below are two triangles.
A
J
C
B L
K
segment AC = segment JL
segment BC = segment KL
segment AB = segment JK
Based on the information given about the triangles, what method could be used to prove the two triangles are
congruent?
a. SSS
c. The triangles cannot be proven congruent.
b. ASA
d. SAS
Standard PPF.651 Draw conclusions based on a set of conditions
2. Is there enough information to prove the two triangles congruent? If yes, write the congruence statement and name
the postulate you would use. If no, write not possible and tell what other information you would need.
Q
|
|
(
)
S
P
R
3. Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence statement and
explain. If no, write not possible and tell what other information you would need.
Given:
(
B
A
C
(
D
4. Write the missing reasons to complete the flow proof.
Given:
Prove:
are right angles,
B
(
)
A
D
C
5. What is the missing reason in the proof?
Given: parallelogram ABCD with diagonal
Prove:
A
B
D
C
Statements
Reasons
1. Definition of parallelogram
1.
2.
2. Alternate Interior Angles Theorem
3. Definition of parallelogram
3.
4.
5.
6.
4. Alternate Interior Angles Theorem
5. Reflexive Property of Congruence
6. ?
a. Reflexive Property of Congruence
b. ASA
c. Alternate Interior Angles Theorem
d. SSS
6. Supply the reasons missing from the proof shown below.
Given:
,
Prove:
|
|
(
(
A
B
D
C
a. ASA; CPCTC
b. SAS; Reflexive Property
c. SSS; Reflexive Property
d. SAS; CPCTC
7. Supply the missing reasons to complete the proof.
Given:
and
Prove:
Q
S
R
P
T
a. ASA; Substitution
b. SAS; CPCTC
c. AAS; CPCTC
d. ASA; CPCTC
8. What is the missing reason in the two-column proof?
Given:
Prove:
bisects
and
bisects
B
<
A
C
>
D
Statements
Reasons
1.
2.
3.
bisects
1. Given
2. Definition of angle bisector
3. Reflexive property
4.
bisects
4. Given
5. Definition of angle bisector
6.
?
5.
6.
a. ASA Postulate
b. SSS Postulate
c. SAS Postulate
d. AAS Theorem
9. Write a proof:
Given:
Prove:
B
C
A
D
Geometry G3 HW 3
Due 10/18
Answer Section
Proofs
1. ANS: A
Look at what parts of the triangles are congruent and label the diagram to help you.
Feedback
A
B
C
D
Correct!
Check which of the parts are congruent.
Have you labeled the diagram with the information given?
Check which parts of the triangles are congruent.
PTS:
OBJ:
STA:
KEY:
2. ANS:
Yes;
1
DIF: Bloom's Level: Comprehension
REF: Mathematics
Describe and apply the properties of similar and congruent figures.
10: 4.1.a
TOP: Geometric Concepts, Properties, and Relationships
congruent triangles | ASA | SSS | SAS
MSC: MA-10-00175
by SAS.
PTS: 1
DIF: L2
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Using the SSS and SAS Postulates
NAT: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
STA: CO 4.3
KEY: SAS | proof | reasoning
MSC: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
3. ANS:
Not possible; you have one pair of congruent angles
and one pair of congruent sides
you would need to know that one more pair of angles are congruent, either
or
to prove the triangles congruent by AAS.
, but
,
PTS: 1
DIF: L2
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem
NAT: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
STA: CO 4.3
TOP: 4-3 Example 3
KEY: multi-part question | AAS | proof | writing in math
MSC: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
4. ANS:
a. Definition of right triangles
b. Converse of Isosceles Triangle Theorem
c. Reflexive property
d. Hypotenuse-Leg Theorem
PTS: 1
DIF: L1
REF: 4-6 Congruence in Right Triangles
OBJ: 4-6.1 The Hypotenuse-Leg Theorem
NAT: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14 | TV.LV20.16 |
TV.LV20.18
STA: CO 4.3
TOP: 4-6 Example 2
KEY: flow proof | HL Theorem | Converse of Isosceles Triangle Theorem | right triangle | proof
MSC: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14 | TV.LV20.16 |
TV.LV20.18
5. ANS: B
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
OBJ: 6-2.2 Properties: Diagonals and Transversals
NAT: NAEP G3f | CAT5.LV20.50 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM | S9.TSK2.PRA |
S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.12 | TV.LV20.14 | TV.LV20.16
STA: CO 4.3
KEY: proof | two-column proof | parallelogram | diagonal
MSC: NAEP G3f | CAT5.LV20.50 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM | S9.TSK2.PRA |
S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.12 | TV.LV20.14 | TV.LV20.16
6. ANS: D
PTS: 1
DIF: L1
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 The Isosceles Triangle Theorems
NAT: NAEP G3f | CAT5.LV20.50 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM | S9.TSK2.PRA |
S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.14 | TV.LV20.16
STA: CO 4.3
TOP: 4-5 Example 1
KEY: segment bisector | isosceles triangle | proof
MSC: NAEP G3f | CAT5.LV20.50 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP | S9.TSK2.GM | S9.TSK2.PRA |
S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.14 | TV.LV20.16
7. ANS: D
PTS: 1
DIF: L1
REF: 4-4 Using Congruent Triangles: CPCTC
OBJ: 4-4.1 Proving Parts of Triangles Congruent
NAT: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
STA: CO 4.3
TOP: 4-4 Example 1
KEY: ASA | CPCTC | proof
MSC: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
8. ANS: A
PTS: 1
DIF: L1
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem
NAT: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
STA: CO 4.3
TOP: 4-3 Example 2
KEY: ASA | proof
MSC: NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
9. ANS:
[4]
Statement
Reason
1.
and
1. Given
2.
3.
4.
[3]
[2]
[1]
2. Reflexive Property
3. ASA
4. CPCTC
correct idea, some details inaccurate
correct idea, not well organized
correct idea, one or more significant steps omitted
PTS:
OBJ:
NAT:
STA:
KEY:
MSC:
1
DIF: L3
REF: 4-4 Using Congruent Triangles: CPCTC
4-4.1 Proving Parts of Triangles Congruent
NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14
CO 4.3
ASA | CPCTC | congruent figures | corresponding parts | rubric-based question | extended response | proof
NAEP G2e | CAT5.LV20.56 | IT.LV16.CP | S9.TSK2.GM | S10.TSK2.GM | TV.LV20.14