M7G1 Students will construct plane figures that meet given conditions.
a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
b. Recognize that many constructions are based on the creation of congruent triangles.
M7G2 Students will demonstrate understanding of transformations.
a. Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations. (Translations and Reflections )
b. Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.
M7G3 Students will use the properties of similarity and apply these concepts to geometric figures.
a. Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts. (Congruent And Similar Triangles )
b. Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures. (Proportions 2 )
c. Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape. (Congruent And Similar Triangles )
M7G4 Students will further develop their understanding of three-dimensional figures.
a. Describe three-dimensional figures formed by translations and rotations of plane figures through space.
b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.
a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
b. Recognize that many constructions are based on the creation of congruent triangles.
M7G2 Students will demonstrate understanding of transformations.
a. Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations. (Translations and Reflections )
b. Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.
M7G3 Students will use the properties of similarity and apply these concepts to geometric figures.
a. Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts. (Congruent And Similar Triangles )
b. Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures. (Proportions 2 )
c. Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape. (Congruent And Similar Triangles )
M7G4 Students will further develop their understanding of three-dimensional figures.
a. Describe three-dimensional figures formed by translations and rotations of plane figures through space.
b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.