This page shows questions in the Geometry Year 1 public release module at MSDE. Geometry
"Geometry Year 1"
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This is a multiple choice question that allows you to select several options.
The figure shows right triangle JLM with segment K M perpendicular to segment J L. Side lengths are given in units.
For which angles in the figure is the sine equal to one half?
Select all that apply.
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This is a drag and drop question that allows you to select text and place it in an appropriate answer space.
The figure shows quadrilateral RSUV with segment R V parallel to segment S U and congruent segments as marked.
Prove that segment R U bisects segment S V by placing the reasons for steps 4 and 5 in the proof.
| Statement | Reason |
| 1) Quadrilateral RSUV with segment R V parallel to segment S U and segment R V congruent to segment S U | 1) Given |
| 2) angle K S U is congruent to angle K V R | 2) Alternate interior angles formed by parallel lines cut by a transversal are congruent. |
| 3) angle S U K is congruent to angle K R V | 3) Alternate interior angles formed by parallel lines cut by a transversal are congruent. |
| 4) triangle S U K is congruent to triangle V R K | |
| 5) segment S K is congruent to segment V K | |
| 6) segment R U bisects segment S V | 6) Definition of bisect |
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This is a test question that allows you to enter extended text in your response.
In the right triangle shown, Trish wants to estimate the degree measure of theta. She knows that 10 is less than or equal to A, which is less than or equal to 11 and that 5 is less than or equal to B, which is less than or equal to 6.
Determine the greatest and least estimates of the degree measure of theta. Explain how you determined each estimate.
Enter your answers and your explanations in the space provided.
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This is a multiple choice question that allows you to select several options.
Parallelogram JKLM is drawn in the coordinate plane. Which transformation must produce a parallelogram that is similar to parallelogram JKLM?
Select all that apply.
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This is a test question that allows you to enter extended text in your response.
Consider triangle R S T, as shown.
In triangle R S T, cosine of R equals three fifths. Find sine of T.
Enter your answer in the box.
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This is a test question that allows you to enter extended text in your response.
The longer base of a trapezoid has endpoints of coordinates negative 2, negative 4 and coordinates 4, 0 The shorter base contains the point coordinates 3, 1
Write an equation of the line that contains the shorter base of the trapezoid. Provide valid mathematical reasoning and calculations to explain how you derived your equation
Enter your equation and your explanation in the space provided.
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This is a fill in the blank question that allows you to enter only numbers.
A circle in the xy-coordinate plane is represented by the equation x squared plus y squared minus 6 x equals 11.
What is the x-coordinate of the center of the circle?
Enter your answer in the box.
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This is a multiple choice question that allows you to select only one option.
Quadrilateral JKLM is graphed in the coordinate plane. Under which transformation would the image of JKLM be similar to JKLM?
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This is a multiple choice question that allows you to select only one option.
The figure shows rectangle PQRS in the first quadrant of a coordinate plane.
Rectangle PQRS is reflected across the x-axis. The image is p prime q prime r prime s prime. Which two further transformations will carry rectangle p prime q prime r prime s prime. back onto rectangle PQRS?
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This is a test question that allows you to enter extended text in your response.
In the given diagram
- B, X, and A are collinear,
- B, Y, and C are collinear, and
- B X equals one third open parenthesis B A close parenthesis and B Y equals one third open parenthesis B C close parenthesis
Prove that line X Y and line A C are parallel.
Enter your proof in the space provided.
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This is a multiple choice question that allows you to select only one option.
Mark, Tom, and Sam are members of a search team. The positions of Tom and Sam are represented in the grid below. Mark started at the same point as Sam and walked two-thirds of the way toward Tom and then stopped.
What are the coordinates of Mark's current location?
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This is a question with 2 parts, including a test question that allows you to enter extended text in your response.
Part A
The Pisces Place is a company that makes fish tanks. Corey has sent the company a special order for a fish tank that is a rectangular prism with an open top. He provides a sketch with the dimensions as shown.
One cubic foot of water is equivalent to 7.48 gallons. If the capacity of the fish tank is 100 gallons, find the maximum possible height for the fish tank. Round your answer to the nearest thousandth of an inch. Show your work.
Enter your answer and your work in the space provided.
Part B
Corey plans to have the completed fish tank sent to his home. A shipping company offers to ship it at a cost of $0.25 per pound.
Corey knows that his fish tank would weigh a total of 1,100 pounds if it were filled to capacity. One cubic foot of water weight 62.4 pounds.
Use this information to calculate the total cost to ship the fish tank when it is empty. Show your work.
Enter your answer and your work in the space provided.
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