School Improvement in Maryland

Public Release Item: Public Release items have appeared on HSA forms and then are released for public viewing and use. Releasing items is one step to ensuring that schools, districts, and other stakeholders understand how the core learning goals are assessed on the HSA.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

Indicator 2.2.1 The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.

Assessment Limits:

  • Students will demonstrate geometric reasoning and justify conclusions. Although the focus is on geometric theory, answers to some items may include a numeric answer.
  • Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.

Selected Response Item - Released in 2003

Right triangle PQR is shown below. QS is perpendicular to PR.

Note: The figure is not drawn to scale.

Which of these is the correct similarity statement involving ?

/share/clg/xml/public_release/mathematics/2003_221_geo07.xml

Correct Answer:
D

Selected Response Item - Released in 2000

Ricardo makes sails for sailboats. A customer places an order for a right triangle sail, as shown below.

Which theorem guarantees that all triangles with the measurements shown above will be congruent?

  1. Angle-Angle-Side (AAS)
  2. Side-Angle-Side (SAS)
  3. Angle-Side-Angle (ASA)
  4. Side-Side-Side (SSS)
/share/clg/xml/public_release/mathematics/2000_221_geo05.xml

Correct Answer:
B

Extended Constructed Response (ECR) Item - Released in 2000

Isosceles triangle ABC is shown below. BD is the angle bisector of angleABC.

Complete the following in the answer box below:
  • Prove that BD bisects AC.
     

/share/clg/xml/public_release/mathematics/2000_221_geo19.xml

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Selected Response Item - Released in 2000

The diagram below shows the rafters for a house and garage. The house rafter is parallel to the garage rafter.

What is the length (x) of the garage rafter? Round the answer to the nearest foot.

  1. 5 feet
  2. 7 feet
  3. 9 feet
  4. 11 feet
/share/clg/xml/public_release/mathematics/2000_221_geo21.xml

Correct Answer:
C

Selected Response Item - Released in 2000

The design for a company’s logo is shown below. angleP is congruent to angleQ is congruent to angleX is congruent to angleY.

What is the length of XZ? Round the answer to the nearest tenth of a centimeter.

  1. 2.2 centimeters
  2. 2.6 centimeters
  3. 3.1 centimeters
  4. 4.2 centimeters
/share/clg/xml/public_release/mathematics/2000_221_geo32.xml

Correct Answer:
C

Selected Response Item - Released in 2000

In the figure below, PQ is parallel to KM.

Which statement must be true about the figure?

  1. ΔLPQ is congruent to ΔPKR
  2. ΔLPQ ~ ΔLKM
  3. ΔPKR is congruent to ΔQRM
  4. ΔPKR ~ ΔQRM
/share/clg/xml/public_release/mathematics/2000_221_geo33.xml

Correct Answer:
B

Student Produced Response (SPR) Item - Released in 2000

A streetlight casts a 10-foot shadow, while a 6-foot person casts a 4-foot shadow. What is the height, in feet, of the streetlight?

/share/clg/xml/public_release/mathematics/2000_221_geo43.xml

Correct Answer:
15

Student Produced Response (SPR) Item - Released in 2005

Look at the figure below.

What is the distance, in inches, between A and B?

/share/clg/xml/public_release/mathematics/2005_221_geo35.xml

Correct Answer:
6

Selected Response Item - Released in 2002

  1. 30°
  2. 50°
  3. 70°
  4. 80°
/share/clg/xml/public_release/mathematics/2002_221_geo03.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2002

An engineering firm wants to build a bridge across the river shown below. An engineer measures the following distances: BC = 1,200 feet, CD = 40 feet, and DE = 20 feet.

Complete the following in the answer box below:
  • Prove is similar to .
  • Railings cost $4 per foot. How much will it cost to put railings on both sides of the bridge? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

/share/clg/xml/public_release/mathematics/2002_221_geo15.xml

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Selected Response Item - Released in 2002

Triangles KOL and MON are shown below.
.

Which of these is needed to prove that the triangles are congruent by Angle-Side-Angle (ASA)?

/share/clg/xml/public_release/mathematics/2002_221_geo22.xml

Correct Answer:
A

Selected Response Item - Released in 2003

A contractor built two triangular supports. He wants both triangular supports to be congruent. Which of these processes will enable the contractor to determine that these two triangular supports are congruent?

  1. measure all three sides of each triangular support
  2. measure all three angles of each triangular support
  3. measure the smallest angle and the longest side in each triangular support
  4. measure the smallest angle and the shortest and longest sides in each triangular support
/share/clg/xml/public_release/mathematics/2003_221_geo24.xml

Correct Answer:
A

Student Produced Response (SPR) Item - Released in 2003

Look at the figure below.

Note: The figure is not drawn to scale.

What is the value of x?

/share/clg/xml/public_release/mathematics/2003_221_geo36.xml

Correct Answer:
17.5

Student Produced Response (SPR) Item - Released in 2001

Steve and Barbara are sitting on opposite ends of a 12-foot-long seesaw. The fulcrum (support) at the center of the seesaw is 3 feet high.


Note: This figure is not drawn to scale.

When Steve's end of the seesaw is touching the ground, how many feet off the ground is Barbara's end of the seesaw?

/share/clg/xml/public_release/mathematics/2001_221_geo33.xml

Correct Answer:
6

Extended Constructed Response (ECR) Item - Released in 2001

Rectangle ABCD is shown below.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

/share/clg/xml/public_release/mathematics/2001_221_geo11.xml

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Student Produced Response (SPR) Item - Released in 2001

A swimmer needs to know the width of a river without having to cross it. She made a diagram below.


Note: This figure is not drawn to scale.

What is the width (w), in meters, of the river?

/share/clg/xml/public_release/mathematics/2001_221_geo32.xml

Correct Answer:
32

Selected Response Item - Released in 2001

A contractor is designing a bridge to go over the lake. The contractor will use the measurements shown below to calculate the length of the bridge. Line ST is parallel to line PQ.


Note: The figure is not drawn to scale.

What is the length (x) of the bridge? Round the answer to the nearest foot.

  1. 10 feet
  2. 11 feet
  3. 24 feet
  4. 38 feet
/share/clg/xml/public_release/mathematics/2001_221_geo46.xml

Correct Answer:
C

Selected Response Item - Released in 2004

Kathryn designs a see-saw, as shown below.

What is the maximum height (x) that the see-saw will reach?

  1. 2.5 feet
  2. 5.0 feet
  3. 6.4 feet
  4. 8.0 feet
/share/clg/xml/public_release/mathematics/2004_221_geo11.xml

Correct Answer:
B

Student Produced Response (SPR) Item - Released in 2004

Two triangles are shown below. ΔPQR ≅ ΔLKM.

What is the measure, in degrees, of angleK?

/share/clg/xml/public_release/mathematics/2004_221_geo13.xml

Correct Answer:
61

Selected Response Item - Released in 2004

A rectangle with area A and perimeter P is cut into two congruent pieces. Which of these must be true?

  1. Each piece has area A⁄2.
  2. Each piece is a triangle.
  3. Each piece is a rectangle.
  4. Each piece has perimeter P⁄2.
/share/clg/xml/public_release/mathematics/2004_221_geo18.xml

Correct Answer:
A

Extended Constructed Response (ECR) Item - Released in 2004

In the figure below, ΔABD and ΔCDB are isosceles triangles. The vertex angles, angleABD and angleCDB and, are congruent as shown below.

Complete the following on a piece of paper and/or in the answer box below:
  • Prove that quadrilateral ABCD is a parallelogram.
     

/share/clg/xml/public_release/mathematics/2004_221_geo21.xml

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Selected Response Item - Released in 2004

A builder receives two shipments of roof trusses (triangular supports). The sides of the triangles have the lengths shown below.

If the measure of angleJ is 30°, what is the measure of angleN?

  1. 30°
  2. 90°
  3. 120°
  4. 150°
/share/clg/xml/public_release/mathematics/2004_221_geo30.xml

Correct Answer:
C

Selected Response Item - Released in 2005

The two pentagons shown below are congruent.

What is the value of x?

  1. 4.8
  2. 5.0
  3. 5.1
  4. 5.3
/share/clg/xml/public_release/mathematics/2005_221_geo02.xml

Correct Answer:
C

Selected Response Item - Released in 2005

Ricardo makes sails for sailboats. A customer places an order for a right triangle sail, as shown below.

Which theorem guarantees that all triangles with the measurements shown above will be congruent?

  1. AAS
  2. SAS
  3. ASA
  4. SSS
/share/clg/xml/public_release/mathematics/2005_221_geo23.xml

Correct Answer:
C

Selected Response Item - Released in 2001

A flagpole casts a shadow 27 feet long. Larry is 6 feet tall and casts a 5-foot shadow.


Note: The figure is not drawn to scale.

How tall is the flagpole? Round the answer to the nearest foot.

  1. 18 feet
  2. 25 feet
  3. 28 feet
  4. 32 feet
/share/clg/xml/public_release/mathematics/2001_221_geo45.xml

Correct Answer:
D

Selected Response Item - Released in 2005

In the figures below, pentagon KLMNO is congruent to pentagon RSTUV.

What is the length of MN?

  1. 2.2 centimeters
  2. 4.0 centimeters
  3. 4.2 centimeters
  4. 7.8 centimeters
/share/clg/xml/public_release/mathematics/2005_221_geo24.xml

Correct Answer:
C

Selected Response Item - Released in 2001

A sail is shown below as triangle RTU. Line SV is a stripe.


Note: The figure is not drawn to scale.

What is the length of line SV?

  1. 4 feet
  2. 6 feet
  3. 8 feet
  4. 10 feet
/share/clg/xml/public_release/mathematics/2001_221_geo40.xml

Correct Answer:
C

Selected Response Item - Released in 2003

Quadrilateral PQRS is shown below.

If quadrilateral WXYZ is congruent to quadrilateral PQRS, what is the measure of   ?

  1. 45°
  2. 70°
  3. 112°
  4. 133°
/share/clg/xml/public_release/mathematics/2003_221_geo03.xml

Correct Answer:
D

Selected Response Item - Released in 2002

A ladder is placed against a fence that is 6 feet tall. The ladder extends 2 feet above the fence and 3 feet behind the fence.

Which proportion can be used to find the distance () between the bottom of the ladder and the bottom of the fence?





/share/clg/xml/public_release/mathematics/2002_221_geo26.xml

Correct Answer:
C

Extended Constructed Response (ECR) Item - Released in 2003

The legs of an ironing board are congruent and bisect each other.

Note: The figure is not drawn to scale.

Complete the following in the answer box below, and/or on a piece of paper.
  • Prove that the ironing board is parallel to the floor.
     
  • Use mathematics to justify that ABCD is a rectangle.
     

/share/clg/xml/public_release/mathematics/2003_221_geo21.xml

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Resources for 2.2.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |