WorksheetsGeometry: Benchmark 1
Total questions: 18
Worksheet time: 12mins
In this figure, s ∥ t. Lines s and t are cut by transversals l and m.
Which pair of angles must be supplementary?
∠2 and ∠3
∠4 and ∠10
∠8 and ∠12
∠7 and ∠15
In this figure, s ∥ t. Lines s and t are cut by transversals l and m.
Which angle must be congruent to ∠1?
∠4
∠3
∠14
∠13
If an angle measures 110°, then it is not acute.
What is the converse of this statement?
If an angle does not measure 110°, then it is acute.
If an angle is not acute, then it measures 110°.
If an angle is acute, then it does not measure 110°.
If an angle is acute, then it does measure 110°.
If two angles are supplementary, then their sum is 180°.
What is the inverse of this statement?
If two angles sum to 180°, then the angles are supplementary.
If two angles are not supplementary, then their sum is not 180°.
If two angles do not sum to 180°, then the angles are supplementary.
If two angles are not supplementary, then their sum is 180°.
Contrapositive: If the temperature is below 71°, then the air conditioner will not come on.
Given the contrapositive, what is the original statement?
If the air conditioner will not come on, then the temperature is below 71°.
If the air conditioner comes on, then the temperature is not below 71°.
If the temperature is below 71°, then the air conditioner will come on.
If the temperature is not below 71°, then the air conditioner will come on.
If a ∥ b, and m∠2 = 122°, what is the m∠3?
(a)
Which image shows two parallel lines cut by a transversal?
Let p = You own a dog.
Let q = You own a pet.
Statement: If you do not own a dog, then you own a pet.
Which of the following is the symbolic representation of the given statement?
∼q → p
∼p → ∼q
q → p
∼p → q
Let p = ∠ C is acute .
Let q = ∠D is obtuse .
Create a symbolic representation of the following argument.
∠ C is acute if and only if ∠ D is obtuse. (a)
∠ C is acute or ∠ D is obtuse. (b)
Therefore, ∠ C is acute and ∠ D is obtuse. (c)
p ⟷ q
p ∨ q
∴ p ∧ q
What is a counterexample to the following statement?
Prime numbers are never even.
15 is not prime number or even.
2 is a prime number and is even.
5 is a prime number and is not even.
26 is not a prime number and is even.
Andrew cut a rectangular piece of wood along a straight line, as shown below.
Andrew calculated that x = 70°. Which of the following statements justifies Andrew's calculations?
Vertical angles are congruent.
Alternate exterior angles are congruent.
Consecutive interior angles are supplementary.
Corresponding angles are supplementary.
Lines p and q are cut by transversal m. What value of x would prove p ∥ q?
(a)
The Venn Diagram below shows relationships between some types of triangles.
Which statement is true based off of the diagram?
All triangles are right.
All isosceles triangles are equilateral.
No equilateral triangles are isosceles.
Some right triangles are isosceles.
What does the shaded area represent in this Venn Diagram?
A and B
A or B
A but not B
not A and not B
Of the thirty-two students in a class, a total of 11 students play football, a total of 16 students play basketball, and 5 students play both sports. Which Venn diagram correctly displays this information?
If m∠4 = m∠8 in the drawing below, which statement can be concluded?
l ⟂ m
l ∥ m
m∠2 = m∠3
∠6 and ∠7 are complementary
The Venn Diagram shows the number of students in a class of 28 students wearing blue jeans, t-shirt and/or tennis shoes in a certain day.
How many students in the class were wearing blue jeans AND tennis shoes on this day?
(a)
In this figure, lines a and b are intersected by line t. Which of these statements proves that lines a and b are parallel?
∠1 ≅ ∠2
∠1 ≅ ∠3
∠2 and ∠3 are complementary.
∠1 and ∠2 are supplementary.
