Download Review for Ch 2 Test

Geometry
Chapter 2 Test Review
Name: _________________________
Date: _________________ Pd: _____
K
1.
Given: m∠4 + m∠6 = 180o
Prove: m∠5 = m∠6
4
5
6
J
L
Subtraction Property
Statements
Reasons
Reflexive Property
1) m∠4 + m∠5 = 180o
1)_______________________
Substitution Property
2) m∠4 + m∠6 = 180o
2)________________________
Given
3) m∠4 + m∠5 = m∠4 + m∠6 3)________________________
Angle Addition Postulate
4) m∠4 = m∠4
4)________________________
Segment Addition Postulate
5) m∠5 = m∠6
5)_________________________
Definition of Complementary
Angles
Linear Pair Postulate
2. Create a symbolic representation for the given argument.
Let p represent ∠A is 90° .
Let q represent ∠B is 90° .
is
if and only if
is
or
Therefore
is
is
is
.
Answer Bank
.
and
is
.
3. Solve the equation. Justify each step.
4. Solve the equation. Justify each step.
5. Solve the equation for r. Justify each step.
Solve for the variables.
6.
7.
20. Write the if-then form, the converse, the inverse and the contrapositive of the following statement. Then
circle whether the statement is true or false.
Vertical angles are congruent
If-then: ___________________________________________________________________________________
______________________________________________________________________________ True
False
Converse: ________________________________________________________________________________
______________________________________________________________________________ True
False
Inverse___________________________________________________________________________________
______________________________________________________________________________ True
False
Contrapositive_____________________________________________________________________________
______________________________________________________________________________ True
21. If p represents “the sun is shining”, and q represents “people will dine outside”, write the following in words:
a) : q → p _____________________________________________________________________
b) : p →: q _____________________________________________________________________
c) Write in symbolic notation: If people dine outside, then the sun is not shining.
False
22. Write the converse of the following statement. If both statements are true, rewrite them as a bi-conditional
statement.
If a ray is a bisects an angle, then the ray cuts the angle into two congruent angles.
Converse: ______________________________________________________________________True or False
Biconditional:______________________________________________________________________________
Quadrilaterals
Parallelograms
Rectangles
Squares
Trapezoids
Kites
23. Use the Venn Diagram above to help you determine whether the following statements are true or false.
Provide a counterexample for questions you believe to be false. Explain those you claim to be true.
a) If a quadrilateral is a rectangle, then it is a parallelogram.
b) Some squares are rectangles.
c) All trapezoids are parallelograms.
24. Use the law of syllogism to write a valid conclusion
If you have a cell phone, then you text your friends. If you text your friends, then you will go to the party.
Conclusion: _______________________________________________________________________________
25. What can you conclude from the following two statements?
If an angle measures less than 90o , then it is acute.
m∠B = 63o
Conclusion: _______________________________________________________________________________
26. Use the following statement: If you are at the skate park, then you are a skateboarder.
Label the Venn Diagram based on your conditional statement.
Using the diagram, write one conclusion, if any, that can be drawn
from the following statements:
a) Bob is at the skate park.___________________________________________
b) Juanita is not a skateboarder._______________________________________
c) Sally is not at the skate park. _______________________________________
d) Billy is a skateboarder.____________________________________________
In the diagram, line QT is perpendicular to line RV, m<PWV = 70. Find the measures of the following:
27. Angle RWS __________
S
R
T
28. Angle SWT __________
U
W
29. Angle QWV __________
30. Angle RWP __________
Q
P
V
Use the diagram to state the postulate that verifies the truth of the statement.
Segment Addition Postulate
A line contains at least two points.
Angle Addition Postulate
Two lines intersect at exactly one point.
Through any two points there exists exactly one
line
A plane contains at least three noncollinear
points.
If two points lie in a plane, then the line
containing them lies in the plane.
The intersection of two planes is a line.
Two lines are perpendicular if they form a right
angle.
31. Line k and line l intersect at point B.
32. Points C, B, and D are on Plane M.
33. DE+EF=DF
34. Points C and F are on line p.