WorksheetsCh. 2 Review
Total questions: 22
Worksheet time: 22mins
Write a conjecture given that △ABC is an equilateral triangle.
It is a right triangle
AB=BC=CA
It has an obtuse angle
If ∠ A and ∠ B are complementary, then m∠ A = 45. Find a counterexample.
m∠ A = 45 when m∠ B = 45
m∠ A = 40 when m∠ B = 140
m∠ A = 40 when m∠ B = 50
Find the next term in the sequence 1, 4, 9, 16, 25 . . .
36
34
35
49
Determine the intersection of lines m and p.
a plane
a line segment
2 points
a point
lines cannot intersect
Complete the following statement: If AB=BC and A, B, and C are collinear, then B is the (a) of 𝐴𝐶.
Name the definition, property, postulate, or theorem that justifies this statement: If x = 2, then 2 = x.
reflexive property
symmetric property
transitive property
distributive property
Name the definition, property, postulate, or theorem that justifies this statement: If x + 3 = y, then x = y – 3.
addition property
distributive property
subtraction property
substitution
Determine whether the conjecture is true or false:
Given: Two planes intersect. Conjecture: The planes can intersect only at one point.
TRUE
FALSE
Identify the conclusion of the statement:
" Either 𝑥=2 or 𝑥=−2 if 𝑥2= 4. "
(HINT: Rewrite the statement in if-then form!)
"x2=4"
"either x=2 or x=-2"
"x=2"
Find the converse of the statement: "If two angles are supplementary and congruent, then they are right angles."
If 2 angles are not right angles, then they are not supplementary and congruent.
If 2 angles are not supplementary and congruent, then they are not right angles.
If 2 angles are right angles, then they are supplementary and congruent.
Use the Law of Detachment to tell whether the following reason is valid...
Given: If you got a speeding ticket, then you drove over the speed limit. Joe drove over the speed limit. Conclusion: Joe got a speeding ticket.
Valid
Not valid
What conclusion follows from these two statements by using the Law of Syllogism?:
A. If a triangle is equilateral, then it has three congruent sides.
B. If all the sides of a triangle are congruent, then each of its angles measures 60.
If a triangle has 3 congruent sides, it is equilateral.
If a triangle is equilateral, then each of its angles measures 60.
If all the sides of a triangle are congruent, then it is equilateral.
Name the definition, property, postulate, or theorem that justifies the statement:
If 𝐷𝐸̅̅̅̅ ≅ 𝐹𝐺̅̅̅̅,𝑡ℎ𝑒𝑛 𝐹𝐺̅̅̅̅≅ 𝐷𝐸
Commutative
Reflexive
Transitive
Symmetric
Name the definition, property, postulate, or theorem that justifies the statement:
If XY = WZ, then XY + TU =WZ + TU.
Subtraction Property
Addition Property
Transitive Property
Reflexive Property
Name the definition, property, postulate, or theorem that justifies the statement:
If m∠1 + m∠2 =180 and m∠2 + m∠3 =180, then ∠1 ≅ ∠3.
Congruent Complements Theorem
Addition Property
Congruent Supplements Theorem
Transitive Property
Name the definition, property, postulate, or theorem that justifies the statement:
If ∠1 and ∠2 are vertical angles, then ∠1 ≅ ∠2.
Reflexive Property
Substitution
Congruent Complements Thm.
Vertical Angles Thm.
If m∠A= 5x-12, m∠B = 2x+18, ∠A and ∠C are supplementary, and ∠B and ∠C are supplementary, find x.
10
2
12
Write the statement "All chickens have two wings" in if-then form.
If an animal has 2 wings, then it is a chicken.
If an animal doesn't have 2 wings, then it is not a chicken.
If an animal is a chicken, then it has 2 wings.
If a chicken has 2 wings, then it is a bird.
Use the Law of Detachment to write a valid conclusion for the given information:
- If a football team wins the Big 10 championship, then they will play in the Rose Bowl.
- Penn State wins the Big 10 championship.
Penn State is a football team
Penn State will play in the Rose Bowl
Penn State wins the Big 10 championship
If a football team wins the Big 10 championship, then Penn State wins the Big 10 championship.
Use the Law of Syllogism to write a valid conclusion for the given information:
(1) If today is Thursday, then Amy is off from work.
(2) If Amy is off from work then she will go to gym to workout.
If today is Thursday, then Amy will go to the gym to workout.
If Amy is off work, then today is Thursday.
No valid conclusion
If today is not Thursday, then Amy is not off work.
Complete the proof by supplying the missing info:
Division Property
Distributive Property
Substitution
Multiplication Property
Complete the proof by filling in the blanks:
4) Def. of Congruent; 5) Congruent Supplements Thm
4) Def of Angle Bisector; 5) Congruent Complements Thm
4) Given; 5) Def of Angle Bisector
4) Def of Angle Bisector; 5) Transitive Prop
