Unit 1 Test Review- Logical Reasoning
Name___________________________ Date __________ Period______
1. Write in the box what each symbol represents.

̅̅̅̅
𝐴𝐵
⃡
𝐴𝐵
||
𝐴𝐵

 A
Script capital
letter or three
capital letters
2. Classify each of the following statements as either a fact or an assumption:
______ All girls wear dresses.
______ All people in Texas ride horses.
______ Travis High School is on Harlem Road.
______ Today is August 4th.
______ Geometry is a requirement for graduation. ______ If I don’t do this review, then I will fail the test.
3. Use the image to the right to answer the following:
The intersection of Plane QXY and plane XWZ. __________________________
⃡ 𝑎𝑛𝑑 𝑅𝑆
⃡ __________________________
The intersection of 𝑃𝑆
All the lines skew to ⃡𝑌𝑍 __________________________
All the lines parallel to ⃡𝑌𝑍 __________________________
Four coplanar points ________________________
4. Write the definition of the following vocabulary terms in your own words:
Segment-__________________________________________________________________
Perpendicular-______________________________________________________________
Coplanar-__________________________________________________________________
Non Collinear-______________________________________________________________
Ray-______________________________________________________________________
Postulate-_________________________________________________________________
Skew-_____________________________________________________________________
5. Write conditional statements for the following.
Hypothesis: A figure is a rectangle. Conclusion: A figure has four right angles.
___________________________________________________________________________________________
Hypothesis: It is raining.
Conclusion: I will need an umbrella.
___________________________________________________________________________________________
6. Determine the validity of each conditional. If false, give a counterexample.
If two lines do not intersect, then they are skew. ____________________________________________________
If I graduate, then I passed Geometry. ____________________________________________________________
7. Given: 3(x-2) +10 –x = 7x – 6
Prove: x = 2
8. Write the following statement and determine the truth value.
If I go to the store, then I will buy food.
Inverse: ________________________________________________________________________________ T or F
Converse: ______________________________________________________________________________ T or F
Contrapositive: __________________________________________________________________________ T or F
9. What two things need to be true in order to write a biconditional?
10. Symbolic Logic
Conditional using P and Q
Inverse of ~𝐾 → 𝑁
Converse of T→ ~𝑅
Contrapositive of ~𝐿 → ~𝑊
Biconditional using P and Q
11. Using the Law of Detachment, what conclusion, if any, can you make from the two given
statements?
If I go to the store, then I will buy candy.
I go to the store.
Conclusion: ______________________________________________________________
12. Use the Law of Detachment and Syllogism to make a conclusion.
If you make below a 75 on the test, then you will retest.
If you retest, then you will have to stay after school.
Cindy made a 62 on the test.
Conclusion: ______________________________________________________________
13. Given the conditional statement and its converse, write the biconditional.
If it has four sides, then it is a quadrilateral.
If it is a quadrilateral, then it has four sides.
____________________________________________________________________________________
14. Base on the picture, determine if the following statements are true or false.
____ Conditional: If three points are collinear, then they are coplanar.
____ Inverse: If three points are non-collinear, then they are non-coplanar.
____Converse: If three points are coplanar, then they are collinear.
____Contrapositive: If three points are non-coplanar, then they are non-collinear.
15. Write a biconditional if possible.