School Improvement in Maryland
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 2.0 Knowledge of Geometry

Topic C. Representation of Geometric Figures

Indicator 1. Represent plane geometric figures

Objective c. Construct triangles

Assessment limit: Construct a triangle congruent to a given triangle

Clarification

Replicating geometric figures through constructions is an important part of geometry. It is through these constructions that students understand the minimum requirements for congruence between polygons. Given a triangle, students will be asked to construct a triangle congruent to a given triangle. When asked to do this on an assessment, the student will be given one side and will need to construct the remaining two sides to complete the duplication. Students may only use the tools of construction to create the copy: compass/straightedge, patty paper, or a MiraTM. On the assessment they will be provided with only a compass and straightedge.

Classroom Example 1

Triangle Congruent to a Given Triangle

Steps for students to construct a triangle congruent to a given triangle using compass and straightedge:

The student will be given triangleKLM and will need to construct a triangle congruent to triangleKLM. One side of the triangle will be given.

triangle KLM

Given that segment RS is the same length as segment ML, construct triangleRST so that it is congruent to triangleKLM.

RS

Students will use SSS (side-side-side) triangle congruence to construct a congruent triangle. One side, segment RS, is congruent to segment ML. Now they will construct the other two sides of triangleRST so that they are congruent to segment KM and segment KL.

Note: Since students will always be given one side, the easiest technique to copy the triangle will be side-side-side triangle congruence.

  1. Use a compass measure the length of segment KM.
  2. Without changing the adjustment the compass, move the stable end to point R and make an arc.
  3. Set the compass at the length of segment KL.
  4. Without adjusting the compass, move the stable end to point S and make an arc.
  5. Make a point where the arcs intersect and label it T.
  6. Connect point T to R and connect T to S.

triangle image

Classroom Example 2

Triangle Congruent to a Given Triangle

Steps for students to construct a triangle congruent to a given triangle using patty paper:

The student will be given triangleKLM and will need to construct a triangle congruent to triangleKLM. One side of the triangle will be given.

triangle KLM

Given that segment RS is the same length as segment ML, construct triangleRST so that it is congruent to triangleKLM.

RS

Students will use SSS (side-side-side) triangle congruence to construct a congruent triangle. One side, segment RS, is congruent to segment ML. Now they will construct the other two sides of triangleRST so that they are congruent to segment KM and segment KL.

  1. Lay the patty paper over segment RS. Mark the endpoints of segment RS on the patty paper.

    example image

  2. Connect R and S to form segment RS.

    example image

  3. Lay the patty paper over triangleKLM. Align segment ML with segment RS. Mark point K on the patty paper.

    example image

  4. Label the mark for point K point T. Connect R with T and S with T using a straightedge.

    example image
/instruction/clarification/mathematics/grade8/xml/2C1c.xml