Download Geometry Diff – Chapter 2 Cumulative Test Review Name

Geometry Diff – Chapter 2 Cumulative Test Review
1.
Name: _____KEY_________
Make a conjecture give that m∠A = m∠B and m∠B = m∠C .
Using the transitive property of equality gives m∠A = m∠C .
2.
If AB || CD and BD || AC , then ABDC is a rectangle. Find a counterexample.
ABDC could be a parallelogram.
3.
Write the statement "An elephant is a mammal." in if-then form.
If an animal is an elephant, then it is a mammal.
4.
Given the statement, "If M is the midpoint of PQ , then PM ≅ MQ ".
(a) Write the converse statement and state if it is true or false.
If PM ≅ MQ , then M is the midpoint of PQ . False
(b)
Write the inverse statement and state if it is true or false.
If M is not the midpoint of PQ , then PM is not congruent to MQ . False
(c)
Write the contrapositive statement and state if it is true or false.
If PM is not congruent to MQ , then M is not the midpoint of PQ . True
5.
Find a counterexample for the statement, "If x 2 = 25 , then x = 5 ".
x = -5
For problems 6 – 12, write the definition, postulate, theorem or property that justifies each statement.
6.
QA = QA
Reflexive Property of Equality.
7.
If AB ≅ BC and CE ≅ BC , then AB ≅ CE .
Transitive Property of Congruence
8.
If Q is between P and R, then PR = PQ + QR .
Segment Addition Postulate
9.
If AB = CD , then AB + EF = CD + EF .
Addition Property of Equality
10. If AB ≅ XY , then XY ≅ AB .
Symmetric Property of Congruence
11. If two angles are vertical, then they are congruent.
Vertical Angles Theorem
12. If ∠1 and ∠2 are right angles, then ∠1 ≅ ∠2 .
All Right Angles are Congruent
Write a two-column proof for the following.
13. Given:
Prove:
(a)
(b)
(c)
(d)
(e)
(f)
3− 8 + 2x = 11+ 6x
−5 + 2x = 11+ 6x
2x = 16 + 6x
−4x = 16
x = −4
Prove:
(d)
(e)
(f)
Prove:
(a)
(b)
(c)
(d)
(e)
(f)
Reasons
Given
Distributive Property
Simplify or Combine Like Terms
Addition Property of Equality
Subtraction Property of Equality
Division Property of Equality
(a)
(b)
(c)
Reasons
Given
Definition of Congruent
Given
(d)
Definition of Midpoint
(e)
(f)
Substitution Property of = or Transitive Property of =
Definition of Congruent
AB ≅ DE
B is the midpoint of AC
E is the midpoint of DF
BC ≅ EF
Statements
AB ≅ DE
AB = DE
B is the midpoint of AC
E is the midpoint of DF
AB = BC
DE = EF
BC = EF
BC ≅ EF
15. Given:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
x = -4
Statements
3− 2 ( 4 − x ) = 11+ 6x
14. Given:
(a)
(b)
(c)
3− 2 ( 4 − x ) = 11+ 6x
AB ⊥ BD
∠EFG and ∠CBD are complementary
∠EFG ≅ ∠ABC
Statements
Reasons
AB ⊥ BD
(a)
∠ABD is a right angle
(b)
(c)
m∠ABD = 90°
(d)
m∠ABC + m∠CBD = m∠ABD
(e)
m∠ABC + m∠CBD = 90°
∠ABC and ∠CBD are complementary (f)
∠EFG and ∠CBD are complementary (g)
(h)
∠EFG ≅ ∠ABC
Given
Definition of Perpendicular Lines
Definition of Right Angles
Angle Addition Postulate
Substitution P. O. E. or Transitive P. O. E.
Definition of Complementary
Given
Congruent Complements Theorem (If two angles
are complementary to the same angles, then the
angles are congruent.)