1. Corresponding Angles
Two lines are cut by a transversal.
You are given:
∠1 ≅ ∠5
Which conclusion can be made?
A. ∠1 and ∠5 are vertical angles
B. The lines are perpendicular
C. The lines are parallel
D. The transversal is parallel to both lines
2. Chain
Given:
∠2 and ∠3 form a linear pair.
m∠2 = 120°
∠3 ≅ ∠6
What can be concluded?
A. Lines are parallel
B. ∠6 = 120°
C. ∠6 = 60°
D. Cannot determine
3. Hidden Proof
Given:
∠1 ≅ ∠8
These angles are alternate exterior angles.
Which theorem applies?
A. Alternate Exterior Angles Theorem
B. Converse of Alternate Exterior Angles Theorem
C. Vertical Angles Theorem
D. CPCTC
4. Angles + Property
Given:
∠1 ≅ ∠4
∠1 and ∠2 are vertical angles.
What must be true?
A. ∠2 ≅ ∠4
B. ∠2 is supplementary to ∠4
C. Lines are perpendicular
D. None
5. Property
Given:
∠A ≅ ∠B
∠B ≅ ∠C
What property justifies:
∠A ≅ ∠C ?
A. Substitution
B. Reflexive
C. Transitive
D. Converse
6. Segment Relationships
Given:
AB = BC
BC = CD
CD = 10
What is AB?
A. 5
B. 10
C. 20
D. Cannot determine
7. Midpoint Reasoning
Given:
M is midpoint of AB.
AB = 26.
Find MB.
8. Angle Bisector
Given:
BD bisects ∠ABC
m∠ABD = 4x + 6
m∠DBC = 7x − 12
Find x.
9. Same-Side Interior Angles
Given:
∠1 and ∠2 are same-side interior angles.
m∠1 = 3x + 10
m∠2 = 5x + 18
The lines are parallel.
Find x.
10. Alternate Interior Angles
Given:
Lines are parallel.
∠1 and ∠2 are alternate interior angles.
m∠1 = 70°
Find m∠2.
11. Multi-Step Proof Chain
Given:
∠1 and ∠2 are vertical angles.
∠2 ≅ ∠5
∠5 and ∠6 are corresponding angles.
What statement must be true?
A. ∠1 ≅ ∠6
B. ∠1 and ∠6 are supplementary
C. Lines are perpendicular
D. Cannot determine
12. Theorem
Given:
∠3 ≅ ∠7
These are corresponding angles.
What conclusion follows?
A. Lines are parallel
B. Angles are supplementary
C. Transversal is perpendicular
D. None
13. Supplementary Angle Reasoning
Given:
∠1 and ∠2 are supplementary.
∠2 and ∠3 are supplementary.
What can be concluded?
A. ∠1 ≅ ∠3
B. ∠1 = 180°
C. ∠2 = 90°
D. Nothing
14. Properties of Parallelograms
Given:
ABCD is a parallelogram.
What must be true?
A. Adjacent sides are congruent
B. Opposite sides are congruent
C. Diagonals are perpendicular
D. Four right angles
15. Properties of Rectangles
Given:
ABCD is a rectangle.
Which statement must be true?
A. All sides are congruent
B. Diagonals are perpendicular
C. Four right angles
D. Adjacent sides are congruent
Answer Key & Explanations
1. C
If corresponding angles are congruent, then the lines are parallel.
This is the Converse of the Corresponding Angles Theorem.
2. C
∠2 and ∠3 form a linear pair:
120 + ∠3 = 180
∠3 = 60
Given ∠3 ≅ ∠6:
∠6 = 60°
3. B
You know alternate exterior angles are congruent.
You're using that information to conclude lines are parallel.
That means the Converse of the Alternate Exterior Angles Theorem.
4. A
Vertical angles:
∠1 ≅ ∠2
Given:
∠1 ≅ ∠4
By Transitive Property:
∠2 ≅ ∠4
5. C
If:
∠A ≅ ∠B
and
∠B ≅ ∠C
then
∠A ≅ ∠C
This is the Transitive Property.
6. B
AB = BC
BC = CD
CD = 10
Therefore:
AB = 10
7. 13
Midpoint means:
AM = MB
AB = 26
26 ÷ 2 = 13
8. x = 6
Angle bisector means:
4x + 6 = 7x − 12
18 = 3x
x = 6
9. x = 19
Same-side interior angles are supplementary:
(3x + 10) + (5x + 18) = 180
8x + 28 = 180
8x = 152
x = 19
10. 70°
Alternate interior angles formed by parallel lines are congruent.
11. A
∠1 ≅ ∠2 (vertical angles)
∠2 ≅ ∠5 (given)
∠5 ≅ ∠6 (corresponding angles)
Therefore:
∠1 ≅ ∠6
12. A
Corresponding angles congruent
↓
Lines parallel
This is the converse theorem.
13. A
If two angles are supplementary to the same angle, they are congruent.
∠1 ≅ ∠3
14. B
A parallelogram always has opposite sides congruent.
The other choices are special cases.
15. C
A rectangle must have four right angles.
The other choices are only true for certain rectangles (like squares).