Download Geometry Essentials Name REVIEW 2.5 – 2.8 For numbers 1 – 4

Geometry Essentials
REVIEW 2.5 – 2.8
Name _____________________________________
For numbers 1 – 4, 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.
2. A line contains exactly one point.
3. Two lines intersect to form right angles.
4. Three collinear points are contained in a plane.
For numbers 5 – 7, solve for x. Find the measure of the indicated angle and give a reason that justifies your work.
5. If m∠1 = (x + 50) and m∠2 = (3x – 20), find m∠1.
x=
m∠1:________________
m∠2:________________
Reason:____________________________________
6. If m∠1 = (2𝑥)° and m∠2 = 𝑥 ° , find m∠1.
x=
m∠1:________________
m∠2:________________
Reason:____________________________________
For numbers 7 – 14, state the definition, property, postulate, or theorem that justifies each statement.
7. If XY = WZ, then XY + TU = WZ + TU
8. If X is the midpoint of ̅̅̅̅
𝐶𝐷 , then ̅̅̅̅
𝐶𝑋 ≅ ̅̅̅̅
𝑋𝐷 .
9. If ∠K ≅ ∠P and ∠P ≅ ∠T, then ∠K ≅ ∠T.
10. If m∠W + m∠H = 90 and m∠H = 20, then m∠W + 20 = 90.
11. If ∠ 1 and ∠ 2 are vertical angles, then ∠ 1 ≅ ∠ 2
12. If ̅̅̅̅
𝐴𝑇 ≅ ̅̅̅̅
𝐷𝑅 then AT = DR.
13. AB + BC = AC
14. If 4x = 20, then x = 5.
15. Complete the proof by supplying the missing information
11
If 4x – 7 = 2x + 4, then x =
Reason Bank:
Given
Addition Property
Congruent complements theorem
Congruent supplements theorem
Definition of complementary angles
Definition of congruent angles
Definition of congruent segments
Definition of supplementary angles
Distributive Property
Division Property
Reflexive Property
Midpoint Theorem/ Definition of midpoint
Multiplication Property
Segment Addition Postulate
Substitution Property
Subtraction Property
Supplement Theorem
Symmetric Property
Transitive Property
Vertical angles theorem
2
Proof
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
16. Given: M is the midpoint of AB
●
A
MB  BX
Prove: AM  BX
●
M
●
B
●
X
Statements
Note: These may be used more than once
or not at all.
Reasons
1. M is the midpoint of ̅̅̅̅
𝐴𝐵
1. ________________________
2. ________________________
2. Midpoint Theorem
3. AM = MB
3. ________________________
4.________________________
4. Given
5. ________________________
5. _________________________
17. Given: 1  2
2  3
3  4
𝑚1 = 23°
3
1
2
4
Prove: 𝑚4 = 23°
Statements
Reasons
1. 1  2
1. __________________________________________
2. 2 3
2. __________________________________________
3. __________________________________________
3. Transitive Property
4. 3  4
4. __________________________________________
5. 1  4
5. __________________________________________
6. __________________________________________
6. Definition of congruent angles
7. __________________________________________
7. Given
8. __________________________________________
8. __________________________________________