GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
DOK3 1 Which counterexample can be used to show that the following conjecture is FALSE? Given: 1 and 2 are adjacent angles. Conjecture: 1 and 2 are supplementary angles.
A.
B.
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C.
D.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
Section 1 2
Mark is asked to prove that ∠4 ≅ ∠6, given that AB || CD, as shown in the diagram above. Mark's proof is shown in the table below. Step in Proof
Statements
1
∠4 ≅ ∠8 therefore m∠4 = m∠8
2
∠8 ≅ ∠6 therefore m∠8 = m∠6
3
If m∠4 = m∠8 and m∠8 = m∠6 then m∠4 = m∠6
∠4 ≅ ∠6 Which reason supports the statement Mark made in step 2 of his work? 4
A. Vertical angles are congruent.
B. Supplementary angles are congruent.
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C. Corresponding
D. Alternate interior
angles formed by parallel lines are congruent.
angles formed by parallel lines are congruent.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
3 The diagram below shows a transversal line crossing through AB and CD. AB is parrallel to CD.
Given the information above, a student makes the claim ∠1 ≅ ∠5. Her work to prove this claim is shown in the table below. Step 1
Statement It is given that AB || CD
2
∠1 ≅ ∠3 therefore m∠1 = m∠3
3
∠3 ≅ ∠5 therefore m∠3 = m∠5
4
If m∠1 = m∠3 and m∠3 = m∠5, then m∠1 = m∠5
Therefore ∠1 ≅ ∠5 Which reason supports the statement she made in step 3 of her work? 5
A. Vertical angles are congruent.
B. Supplementary angles are congruent.
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C. Corresponding
D. Alternate interior
angles formed by two parallel lines are congruent.
angles formed by two parallel lines are congruent.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
4 The proof below shows that alternate interior angles are congruent when two parallel lines are cut by a transversal.
STATEMENTS REASONS 1. Lines r and s are parallel lines cut by the transversal t. Given 2. ∠1 ≅ ∠6 3. ∠1 ≅ ∠3 4. ∠6 ≅ ∠3 Part A: Which is the missing reason in step 2?
Transitive property
Part B: Which is the missing reason in step 3?
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
5 Given: ABCD is a parallelogram Prove: ΔABC ≅ ΔCDA
Based on the information shown above, Brandon started to write the proof below. Statements 1) ABCD is a parallelogram 2)
4)
Reasons 1) Given 2) Opposite sides of a parallelogram are congruent. 3) When a transversal crosses parallel lines, alternate interior angles are congruent. 4) Reflexive Property
5) ΔABC ≅ ΔCDA
5) SAS Postulate
3)
In order to show that ΔABC ≅ ΔCDA according to the reasons provided, which three statements listed below will Brandon need to use to complete his proof?
A. ∠BCD ≅ ∠DAB B. BC ≅ AD E. ∠ABC ≅ ∠CDA F. AC ≅ AC
C. ∠BAC ≅ ∠DCA D. AB ≅ CD
6 Based on the following figure, determine which values below are correct. Select all that apply.
A. x = 4 E. m∠ACB = 63°
B. x = 6 F. m∠ACB = 81°
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C. x = 9
D. m∠ACB = 51°
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
7 Examine the following figure.
If JL = 16, KM = 4x – 1, and KM is a perpendicular bisector of JL determine which of the following values is/are correct. Select all that apply.
A. x = 3 E. perimeter of
B. JK = 11 C. KM = 15 F. perimeter of ΔJKL
ΔKLM = 22
D. KL = 17
= 50
8 In the figure below, line m || line n and line p || line q.
If m∠1 = 16x + 18 and m∠2 = 24x + 2, determine which of the following angle measures is/are correct. Select all that apply.
A. m∠1 = 50°
B. m∠2 = 98°
9 If T is the midpoint of true?
A.
C. m∠3 = 82°
D. m∠4 = 130°
and V lies between R and T, which statement must be
B.
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C.
D.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
10 Given: PQRS is a parallelogram; S, P, and T are collinear. Prove: 1 4.
Statements
Reasons
1. PQRS is a parallelogram; S, P, and T 1. Given are collinear 2. Definition of a parallelogram 2. 3 3. Parallel lines cut by a transversal form 3. 1 congruent corresponding angles 4. 4. Definition of a parallelogram 5. 4 3 5. ? 6. 1 4 6. Transitive property of congruence Which reason could be used to justify Statement 5?
A. B. C. D.
Angles that are supplements of the same angle are congruent to each other. Parallel lines cut by a transversal form congruent alternate interior angles. Parallel lines cut by a transversal form congruent corresponding angles. Intersecting lines form congruent vertical angles.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
intersects 11 In the figure below, ABCE is a parallelogram, CDE is a triangle, and The proof shown below the figure demonstrates that the measure is 34°.
Which reason BEST supports Statement 2 of the proof?
A. Alternate exterior angles formed by the intersection of a transversal with two parallel lines are congruent. B. Corresponding angles formed by the intersection of a transversal with two parallel lines are congruent. C. Two adjacent angles formed by the intersection of two line segments are supplementary. D. The opposite angles of a parallelogram are congruent.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
12 Mandy was working on this proof: In these figures,
What is the missing statement for the last step of Mandy’s proof?
A. B. C. D.
Definition of perpendicular lines The transitive property of equality If 2 angles are congruent to equal angles, then the 2 angles are congruent. If 2 angles are complementary to congruent angles, then the 2 angles are congruent.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
DOK1 13 In the figure below, line a || line b.
If m∠2 = 78°, which of the following angles also measure 78°? Select all that apply.
A. ∠3 E. ∠7
B. ∠4 F. ∠8
14 In the figure below,
C. ∠5
D. ∠6
C. If two parallel
D. If two parallel
is parallel to
Which statement proves that
A. If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
B. If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.
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lines are cut by a transversal, the corresponding angles are congruent.
lines are cut by a transversal, the vertical angles are congruent.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
15 In the figure below, Angle 1 is congruent to Angle 2.
What reason can be used to prove that m is parallel to n?
A. If a pair of vertical B. If a pair of angles C. If a pair of angles D. If two lines are angles is congruent, then the lines forming them are parallel.
formed by a transversal is corresponding and supplementary, then the two lines are parallel.
is congruent and the sum of their measures is 180º, then the lines forming the angles are parallel.
intersected by a transversal, and a pair of corresponding angles is congruent, then the two lines are parallel.
16 What conclusion would be true given the hypothesis “If Angle 1 is congruent to Angle 2, and Angle 2 is congruent to Angle 3, then . . .”?
A. the measure of Angle 1 is greater than Angle 3.
B. the measure of Angle 1 is less than Angle 3.
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C. Angle 1 is
D. Angle 1 is
supplementary to Angle 3.
congruent to Angle 3.
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GCO9 HWQuestions
Assessment ID:
ib.249472
Directions: Answer the following question(s).
17 A section of a leaded glass window is shown below.
Given: • Each piece of lead in the glass is a straight line segment. • • Which justification proves that
A. addition property
B. transitive property C. vertical angles are D. alternate interior congruent
angles are congruent
18 If two angles are supplementary to the same angle, the two angles are congruent. Which of the following assumptions can be used to do a proof by contradiction?
A. assume the two angles are not congruent
B. assume the two angles are supplementary to a different angle
C. assume the two angles are complementary to the same angle
D. assume the two angles are congruent to supplementary angles
19 Which property is illustrated by the statement below about congruence of angles? If
A. associative
B. reflexive
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C. symmetric
D. transitive
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