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Name: ________________________ Class: ___________________ Date: __________ ID: A
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CH 2 Test Review
Making Conjectures: Conjectures about Angles Formed by Parallel Lines Cut by a Transversal
Use the given information to determine the measures of all unknown angles in each figure. Give a
supporting reason. Use complete sentences to explain how you found your answers
m∠4 = 65°
Angle Measure Reason
m∠1 =
m∠2 =
m∠3 =
m∠4 = 65°
m∠5 =
m∠6 =
m∠7 =
m∠8 =
1. m∠6 = 89°
Angle Measure Reason
=
=
=
=
=
m∠6 = 89°
=
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2. m∠4 = 95°
Angle measure Reason:
m∠1 =
m∠2 =
m∠3 =
m∠4 = 95°
m∠5 =
m∠6 =
m∠7 =
m∠8 =
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Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Same-Side Interior Angle
Theorem, and Same-Side Exterior Angle Theorem
Prove each statement using the indicated type of proof.
Use a paragraph proof to prove the Alternate
Interior Angles Theorem. In your proof, use
the following information and refer to the
diagram.
Given: a Ä b, c is a transversal
Prove: ∠2 ≅ ∠8
3.
Use a two-column proof to prove the Alternate
Exterior Angles Theorem. In your proof, use the
following information and refer to the diagram.
Given: r Ä s, t is a transversal
Prove: ∠4 ≅ ∠5
Statements Reasons
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A Reversed Condition: Parallel Line Converse Theorems
Write the converse of each statement.
EXAMPLE:
If a triangle has three congruent sides, then the triangle is an equilateral triangle.
Converse: If a triangle is an equilateral triangle, then the triangle has three congruent sides.
.
4. If a figure is a rectangle, then it has four sides.
.
5. If two angles in a triangle are congruent, then the triangle is isosceles.
.
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If two lines, cut by a transversal, form same-side
exterior angles that are supplementary, then the lines
are parallel.
Given: ____________________________________
Prove:____________________________________
.
6.
If two lines, cut by a transversal, form alternate interior
angles that are congruent, then the lines are parallel.
Given: ____________________________________
Prove:____________________________________
.
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Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Same-Side Interior Angle
Theorem, and Same-Side Exterior Angle Theorem
Use the diagram to write the “given” and “prove” statements for each theorem.
EXAMPLE: If two parallel lines are cut by a transversal, then the exterior angles on the same side of the
transversal are supplementary.
Given: r Ä c, n is a transversal
Prove: ∠1 and ∠7 are supplementary or ∠2 and
∠8 are supplementary
7.
If two parallel lines are cut by a transversal, then the
alternate interior angles are congruent.
Given: ____________________________________
Prove:____________________________________
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A Reversed Condition: Parallel Line Converse Theorems
Prove each statement using the indicated type of proof.
Use a paragraph proof to prove the Alternate Exterior Angles Converse Theorem. In your proof, use the
following information and refer to the diagram.
Given: ∠4 ≅ ∠5, j is a transversal
Prove: p Ä x
8. Use a two column proof to prove the Alternate Interior Angles Converse Theorem. In your proof, use the
following information and refer to the diagram.
Given: ∠2 ≅ ∠7, k is a transversal
Prove: m Ä n
Statements Reasons
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9. Use a flow chart to prove the Same Side Interior Angles Converse Theorem. In your proof, use the following
information and refer to the diagram.
Given: ∠6 and ∠7 are supplementary, e is a transversal
Prove: f Ä g
Define the reasons on the Word Bank below::
∠5 and ∠6 are a linear pair
∠6 and ∠7 are supplementary
∠5 and ∠6 are supplementary
g II f
∠5 ≅ ∠7
Corresponding Angle Postulate-
____________________________________
______________________________
Definition of linear pair
____________________________________
______________________________
Given
____________________________________
______________________________
Linear Pair Postulate
____________________________________
______________________________
Substitution Property
____________________________________
______________________________
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Many Sides: Naming Geometric Figures
Classify each polygon shown.
Example
triangle
10. ____________________
11. ____________________
12. ____________________
13. ____________________
14. ____________________
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15. ____________________
16. ____________________
Quads and Tris: Classifying Triangles and Quadrilaterals
Draw an example of each term.
17. equiangular triangle
.
18. scalene triangle
.
19. right triangle
.
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20. In the figure, line c is parallel to line d and m∠3 = 26°. Determine the measure of ∠6 using the
Corresponding Angle Postulate and any other theorems, postulates, or properties.
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21.
Use the figure to prove the Alternate Interior Angle
Converse Theorem.
Given: ∠4 ≅ ∠6
Prove: ™ Ä m
Define each reason on the Word bank below:
Corresponding Angle Converse Postulate
___________________________________________________________________________
_______________________________________________________________
Given
___________________________________________________________________________
_______________________________________________________________
Transitive Property
___________________________________________________________________________
_______________________________________________________________
Vertical Angle Theorem
___________________________________________________________________________
_______________________________________________________________
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22. The lines shown in the figure are parallel, and m∠1 = 102°. Determine the missing angle measures without
using a protractor. Explain how you calculated your answers.
Statements Reasons
m∠ 1 = 102°
m∠ 2 =
m∠ 3 =
m∠ 4 =
m∠ 5 =
m∠ 6 =
m∠ 7 =
m∠ 8 =
.
23. Consider the statement “If a quadrilateral is a square, then the quadrilateral is a rectangle.”
a. Identify the hypothesis of the statement.
b. Identify the conclusion of the statement.
c. Write the converse of the statement.
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Making Conjectures: Conjectures about Angles Formed by Parallel Lines Cut by a Transversal
24. Construct line p parallel to line b such that line m is a transversal.
.
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Solve for x in each figure. Show all your work. Give the measurement of all angles; Explain your
reasoning.
.
25.
Measure Reason
m∠1 =
m∠2 =
m∠3 =
m∠4 =
m∠5 =
m∠6 =
m∠7 =
m∠8 =
26.
Measure Reason
m∠1 =
m∠2 =
m∠3 =
m∠4 =
m∠5 =
m∠6 =
m∠7 =
m∠8 =
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.
27. Use the figure to determine the measure of each indicated angle. SHOW ALL YOUR WORK.
a. m∠EGA= _____
b. m∠CHF= _____
c. m∠FHD= _____
d. m∠EGB= _____
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A Reversed Condition: Parallel Line Converse Theorems
28. Use the figure to write the postulate, theorem, or converse theorem that justifies each statement.
a. m∠1 = m∠8, so a Ä b - __________________________________________________
b. m∠4 + m∠6 = 180°, so a Ä b- _____________________________________________
c. a Ä b, so m∠3 = m∠7- __________________________________________________
d. m∠2 + m∠8 = 180°, so a Ä b- _____________________________________________
e. m∠4 = m∠5, so a Ä b- __________________________________________________
f. a Ä b , so m∠3 + m∠5 = 180°- _____________________________________________
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29. Use the given information to determine the pair of lines that are parallel. Write the postulate or theorem that
justifies your answer.
a. m∠4 = m∠5- _________________________________________________________
b. m∠2 + m∠12 = 180°- __________________________________________________
c. m∠7 = m∠11- _______________________________________________________
d. m∠8 + m∠10 = 180°- __________________________________________________
e. m∠1 + m∠7 = 180°- ___________________________________________________
f. m∠2 = m∠11- ________________________________________________________
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CH 2 Test Review
Answer Section
1. ANS: m∠1 = 89°, m∠2 = 91°, m∠3 = 89°, m∠4 = 91°, m∠5 = 91°, m∠7 = 91°, m∠8 = 89°
PTS: 1 REF: Ch2.2 TOP: Skills Practice
2. ANS: m∠1 = 85°, m∠2 = 95°, m∠3 = 85°, m∠5 = 85°, m∠6 = 95°, m∠7 = 85°, m∠8 = 95°
PTS: 1 REF: Ch2.2 TOP: Skills Practice
3. ANS:
Statements Reasons
1. r Ä s, t is a transversal
2. ∠4 ≅ ∠2
3. ∠2 ≅ ∠5
4. ∠4 ≅ ∠5
1. Given
2. Corresponding Angles Postulate
3. Vertical Angles Congruence Theorem
4. Transitive Property
PTS: 1 REF: Ch2.3 TOP: Skills Practice
4. ANS:
Converse: If a figure has four sides, then it is a rectangle.
PTS: 1 REF: Ch2.4 TOP: Skills Practice
5. ANS:
Converse: If a triangle is isosceles, then two angles in the triangle are congruent.
PTS: 1 REF: Ch2.4 TOP: Skills Practice
6. ANS:
Given: a is a transversal; ∠3 ≅ ∠6 or ∠4 ≅ ∠5
Prove: b Ä c
PTS: 1 REF: Ch2.4 TOP: Skills Practice
7. ANS:
Given: a Ä z, d is a transversal
Prove: ∠2 ≅ ∠7 or ∠6 ≅ ∠3
PTS: 1 REF: Ch2.3 TOP: Skills Practice
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8. ANS:
Statements Reasons
1. ∠2 ≅ ∠7 and line k is a transversal
2. Angles 5 and 2 are vertical angles
3. ∠5 ≅ ∠2
4.∠5 ≅ ∠7
5. Angles 5 and 7 are corresponding angles
6. m Ä n
1. Given
2. Definition of vertical angles
3. Vertical Angles Congruence Theorem
4. Transitive Property
5. Definition of corresponding angles
6. Corresponding Angles Converse Postulate
PTS: 1 REF: Ch2.4 TOP: Skills Practice
9. ANS:
∠6 and ∠7 are supplementary- Given
∠5 and ∠6 are a linear pair- Definition of linear pair
∠5 and ∠6 are supplementary- Linear Pair Postulate
∠5 ≅ ∠7 - Corresponding Angle Postulate
g II f - Substitution Property
PTS: 1 REF: Ch2.4 TOP: Skills Practice
10. ANS:
octagon
PTS: 1 REF: Ch2.5 TOP: Skills Practice
11. ANS:
pentagon
PTS: 1 REF: Ch2.5 TOP: Skills Practice
12. ANS:
hexagon
PTS: 1 REF: Ch2.5 TOP: Skills Practice
13. ANS:
quadrilateral
PTS: 1 REF: Ch2.5 TOP: Skills Practice
14. ANS:
nonagon
PTS: 1 REF: Ch2.5 TOP: Skills Practice
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15. ANS:
decagon
PTS: 1 REF: Ch2.5 TOP: Skills Practice
16. ANS:
hexagon
PTS: 1 REF: Ch2.5 TOP: Skills Practice
17. ANS:
PTS: 1 REF: Ch2.6 TOP: Skills Practice
18. ANS:
PTS: 1 REF: Ch2.6 TOP: Skills Practice
19. ANS:
PTS: 1 REF: Ch2.6 TOP: Skills Practice
20. ANS:
By the Corresponding Angle Postulate and the definition of congruent angles, m∠3 = m∠7. By the Linear
Pair Postulate and the definition of supplementary angles, m∠6 + m∠7 = 180°. Using the Substitution
Property, m∠6 + m∠3 = 180°. Then m∠6 = 180° − m∠3 = 180° − 26°. Thus, m∠6 = 154°.
PTS: 1 REF: Ch2.1 TOP: Mid Ch Test
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21. ANS:
Students may use a flow chart or a two-column or paragraph proof. The flow chart proof is provided.
Students only need to use one method.
PTS: 1 REF: Ch2.3 TOP: End Ch Test
22. ANS:
m∠2 = 78° because ∠1 and ∠2 are supplementary angles.
m∠3 = 102° because ∠3 and ∠2 are supplementary angles.
m∠4 = 78° because ∠1 and ∠4 are supplementary angles.
m∠5 = 102° because ∠1and ∠5 are congruent corresponding angles.
m∠6 = 78° because ∠4 and ∠6 are congruent alternate interior angles.
m∠7 = 102° because ∠1and ∠7 are congruent alternate exterior angles.
m∠8 = 78° because ∠4 and ∠8 are congruent corresponding angles.
PTS: 1 REF: Ch2.6 TOP: End Ch Test
23. ANS:
a. a quadrilateral is a square
b. the quadrilateral is a rectangle
c. If a quadrilateral is a rectangle, then the quadrilateral is a square.
PTS: 1 REF: Ch2.1 TOP: Standard Test
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24. ANS:
PTS: 1 REF: Ch2.2 TOP: Assignment
25. ANS:
7x − 14° = 5x + 18°
2x = 32°
x = 16°
PTS: 1 REF: Ch2.2 TOP: Assignment
26. ANS:
3x + 4x + 5° = 180°
7x = 175°
x = 25°
PTS: 1 REF: Ch2.2 TOP: Assignment
27. ANS:
a.11x + 4° + 5x = 180°
16x = 176°
m∠EGA = 11(11°) + 4 = 125°
x = 11°
b. m∠CHF = (5 ⋅ 11)° = 55°
c. m∠FHD = m∠EGA = 125°
d. m∠EGB = m∠CHF = 55°
PTS: 1 REF: Ch2.3 TOP: Assignment
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28. ANS:
a. Alternate Exterior Angles Converse Theorem
b. Same-Side Interior Angles Converse Theorem
c. Corresponding Angles Postulate
d. Same-Side Exterior Angles Converse Theorem
e. Alternate Interior Angles Converse Theorem
f. Same-Side Interior Angles Theorem
PTS: 1 REF: Ch2.4 TOP: Assignment
29. ANS:
a. x Ä y; Alternate Interior Angles Converse Theorem
b. x Ä z; Same-Side Exterior Angles Converse Theorem
c. y Ä z; Corresponding Angles Converse Postulate
d. y Ä z; Same-Side Interior Angles Converse Theorem
e. x Ä y; Same-Side Exterior Angles Converse Theorem
f. x Ä z; Alternate Exterior Angles Converse Theorem
PTS: 1 REF: Ch2.4 TOP: Assignment