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G.CO.C.10

22 Results Found

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8th Grade Math

Students make several advances in their algebraic reasoning as they solve systems of linear equations, use functions to describe relationships, and analyze two- and three-dimensional figures.

Geometry

Students further their understanding of geometric relationships and learn to make formal mathematical arguments about geometric situations, with a heavy emphasis on transformations and proofs.

10th Grade - Constructions, Proof, and Rigid Motion

Students use the properties of circles to construct and understand different geometric figures, and lay the groundwork for constructing mathematical arguments through proof.

10th Grade - Congruence in Two Dimensions

Students identify, perform, and algebraically describe rigid motions to establish congruence of two dimensional polygons, including triangles, and develop congruence criteria for triangles.

8th Grade - Transformations and Angle Relationships

Students investigate congruence and similarity by studying transformations of figures in the coordinate plane, and apply these transformations to discover new angle relationships.

10th Grade - Dilations and Similarity

Students use constructions to explore dilations in order to define and establish similarity, and they prove and use similarity criterion and theorems in the solution of problems.

10th Grade - Right Triangles and Trigonometry

Students develop an understanding of right triangles through an introduction to trigonometry, building an appreciation for the similarity of triangles as the basis for developing the Pythagorean theorem.

10th Grade - Polygons and Algebraic Relationships

Students connect algebra to geometric concepts with polygons as they explore the distance formula, slope criteria for parallel and perpendicular lines, and learn to calculate and justify the area and perimeter of polygons.

10th Grade - Three-Dimensional Measurement and Application

Students extend their understanding of circles, volume, and surface area into modeling situations, formula analysis, and deeper conceptual understandings.

Geometry - Unit 2: Congruence in Two Dimensions - Lesson 2

Prove interior and exterior angle relationships in triangles.

Geometry - Unit 4: Right Triangles and Trigonometry - Lesson 3

Define the relationship between side lengths of special right triangles.

Geometry - Unit 1: Constructions, Proof, and Rigid Motion - Lesson 5

Construct the altitudes and perpendicular bisectors of sides of triangles.

Geometry - Unit 3: Dilations and Similarity - Lesson 6

Prove that a line parallel to one side of a triangle divides the other two sides proportionally.

Geometry - Unit 4: Right Triangles and Trigonometry - Lesson 6

Define and calculate the sine of angles in right triangles. Use similarity criteria to generalize the definition of sine to all angles of the same measure.

Geometry - Unit 5: Polygons and Algebraic Relationships - Lesson 7

Algebraically verify midsegment, median, and parallel line relationships in triangles.

Geometry - Unit 4: Right Triangles and Trigonometry - Lesson 7

Define and calculate the cosine of angles in right triangles. Use similarity criteria to generalize the definition of cosine to all angles of the same measure.

Geometry - Unit 4: Right Triangles and Trigonometry - Lesson 8

Derive the relationship between sine and cosine of complementary angles in right triangles, and describe sine and cosine as angle measures approach 0°, 30°, 45°, 60°, and 90°.

Geometry - Unit 4: Right Triangles and Trigonometry - Lesson 9

Describe and calculate tangent in right triangles. Describe how the value of tangent changes as the angle measure approaches 0°, 45°, and 90°.

Geometry - Unit 6: Three-Dimensional Measurement and Application - Lesson 11

Identify cross-sections of pyramids and use the relationships between the cross-sections to determine the volume of truncated cones and pyramids.

Geometry - Unit 2: Congruence in Two Dimensions - Lesson 11

Prove and apply that the points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

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