Unit 1- Geometry

This unit focuses on how to teach students to draw geometric figures using rulers and protractors with an emphasis on triangles. Students will also explore two-dimensional cross-sections of cylinders, cones, pyramids, and prisms. Their knowledge from 6th grade will help when they are learning to write and solve equations involving angle relationships and when solving engaging problems that require determining the area, volume, and surface area of fundamental solid figures. This unit also requires students to know and use the formula for the circumference and area of a circle.

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**MGSE7.G.2** Explore various geometric shapes with given conditions. Focus on creating triangles from three measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

**MGSE7.G.3** Describe the two-dimensional figures (cross-sections) that result from slicing threedimensional figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres. Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume.

**MGSE7.G.4 **Given the formulas for the area and circumference of a circle, use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

**MGSE7.G.5** Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

**MGSE7.G.6** Solve real‐world and mathematical problems involving area, volume, and surface area of two‐ and three‐dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Understand congruence and similarity using physical models, transparencies, or geometry software.

**MGSE8.G.1 **Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.

**MGSE8.G.2.** Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

**MGSE8.G.3** Describe the effect of dilations, translations, rotations, and reflections on two‐ dimensional figures using coordinates.

**MGSE8.G.4** Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them.

**MGSE8.G.5.** Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. Understand and apply the Pythagorean Theorem.

**MGSE8.G.6.** Explain a proof of the Pythagorean Theorem and its converse.

**MGSE8.G.7.** Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

**MGSE8.G.8.** Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

**MGSE8.G.9** Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.