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Geometry
REVIEW 2.5 – 2.8
Name _____________________________________
For numbers 1 – 3, determine if the statement is always (A), sometimes (S), or never (N) true.
1. If two points lie in a plane, then the entire line containing those points lies in that plane.
Always
2. A line contains 4 points.
Sometimes: A line contains at least 2 points, but can contain more
3. Two lines intersect to form right angles.
Sometimes: only when the lines are perpendicular
4. Three noncollinear points are contained in Plane Y. Always
For numbers 5 – 7, find the measure of the indicated angle and name the theorems that justify your work.
5. If m∠1 = (x + 50) and m∠2 = (3x – 20), find m∠1.
Vertical Angles Thm
X=35
85
6. If m∠1 is twice m∠2, find m∠1.
Supplement Thm
120
7. If ∠ABC ≅ ∠EFG and m∠ABC = 41, find m∠GFH.
Congruent Complement Thm: If two angles are complements of the same angle,
than they are congruent to each other.
49
For numbers 8 – 13, state the definition, property, postulate, or theorem that justifies each statement.
8. If X is the midpoint of ̅̅̅̅
𝐶𝐷 , then ̅̅̅̅
𝐶𝑋 ≅ ̅̅̅̅
𝑋𝐷 .
Midpoint Thm
9. If ∠K ≅ ∠P and ∠P ≅ ∠T, then ∠K ≅ ∠T.
Transitive Thm
10. If m∠W + m∠H = 90 and m∠H = 20, then m∠W + 20 = 90.
Substitution
11. If ∠A and ∠B are complementary, ∠C and ∠D are complementary, and
∠A ≅ ∠C, then ∠B ≅ ∠D.
12. If ̅̅̅̅
𝐴𝑇 ≅ ̅̅̅̅
𝐷𝑅 then AT = DR.
13. AB + BC = AC
Congruent Complements Thm
Def of Congruence
Segment Addition
14. Complete the proof by supplying the missing information
11
If 2x – 7 = 4, then x =
2
Reason Bank:
Proof
Statements
Reasons
1. 2x-7=4
1. Given
2. 2x-7+7=4+7
2. Addition
3. x=11/2
3. Division
15. Given: M is the midpoint of AB
MB  BX
Prove: AM  BX
●
A
●
M
●
B
●
X
Statements
Reasons
1. M is the midpoint of AB
1. Given____________________
2. AM = MB
2.Midpoint Thm______________
̅̅̅̅̅ ≅ ̅̅̅̅̅
3.𝐴𝑀
𝑀𝐵
3. Def of Congruent___________
̅̅̅̅̅ ≅ 𝐵𝑋
̅̅̅̅
4. .𝑀𝐵
4. Given
̅̅̅̅̅ ≅ 𝐵𝑋
̅̅̅̅
5. 𝐴𝑀
5. TransitiveProperty__________
16. Given: 1  2
2  3
3  4
Prove: 1  4
Statements
Addition Property
Congruent complements theorem
Congruent supplements theorem
Definition of complementary angles
Definition of congruent angles
Definition of congruent segments
Definition of midpoint
Definition of supplementary angles
Distributive Property
Division Property
Reflexive Property
Midpoint Theorem
Multiplication Property
Segment Addition Postulate
Substitution Property
Subtraction Property
Supplement Theorem
Symmetric Property
Transitive Property
Vertical angles theorem
3
1
2
Reasons
1. 1  2
1.
Given
2. 2 3
2.
Given
3. 1 3
3.
Transitive
4. 3  4
4.
Given
5. 1  4
5.
Transitive
4