E1.2 Identify and construct congruent triangles, rectangles, and parallelograms.
Skill: Identifying Congruent Triangles
To identify congruent triangles, students can superimpose the angles of the triangles to determine if they are the same. Students can then superimpose the corresponding sides of the triangles to determine if the lengths of the two line segments are the same.
Skill: Identifying Congruent Rectangles
To identify congruent rectangles, students can determine if each corresponding angle measures 90°. Students can then superimpose the corresponding sides of the rectangles to determine if they are the same. In addition, students can overlay the two rectangles to determine if the corresponding opposite sides are parallel by checking to see if the distance between them remains constant.
Skill: Identifying Congruent Parallelograms
To identify congruent parallelograms, students can superimpose the corresponding angles of the parallelograms to determine if they are the same. Students can then superimpose the corresponding sides of the parallelograms to determine if the length of the two line segments is the same. In addition, students can overlay the two parallelograms to determine if the corresponding opposite sides are parallel by checking to see if the distance between them remains constant.
Skill: Constructing Congruent Triangles
To construct two congruent triangles, students can use a protractor to draw corresponding angles such that the distance between the line segments at their points of intersection is the same. Students can then draw the corresponding sides of the triangles with a ruler, making sure that the length of the two line segments of the triangles is the same.
Example of construction of congruent triangles when the measure of the sides is known.
Example of construction of congruent triangles when side and angle measures are known.
Skill: Building Congruent Rectangles
To construct two congruent rectangles, students can use a protractor to draw two corresponding angles such that each measure 90°. Students can then use a ruler to draw two corresponding sides such that the length of the two line segments is the same. In addition, students can use a ruler to draw two corresponding opposite sides that are parallel and where the distance between them remains constant.
For more information on using a protractor, please see Teacher Supports E2.4 in Grade 5.
For more information on using a ruler, please see Teacher Supports E2.3 in Grade 2.
Example of construction of congruent rectangles.
Skill: Constructing Congruent Parallelograms
To construct two congruent parallelograms, students can use a protractor to draw corresponding angles such that the distance between the line segments at their point of intersection is the same. Students can then use a ruler to draw the two corresponding sides of the parallelograms whose two line segments are the same length. In addition, students can superimpose the two rectangles and use a ruler to draw two corresponding opposite sides that are parallel and have a constant the distance between them remaining constant.