Cluster Note: Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. G.CO.9 theorems about lines and angles. Note: This is an overarching standard that will Students will base this new learning on what they know about : Theorems include: vertical angles are be revisited throughout the course. linear congruent; when a transversal crosses parallel supplementary and complementary lines, alternate interior angles are congruent See the skills and knowledge that are angles and corresponding angles are congruent; stated in the Standard. Parallel lines cut by a transversal points on a perpendicular bisector of a line This is an opportunity to also include same segment are exactly those equidistant from the side interior (consecutive) angles and segment’s endpoints. alternate exterior angles in the theorems from parallel G.CO.10 Prove theorems about triangles. Ability to construct a using one of a Theorems include: measures of interior angles variety of methods of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Note: Implementation of this standard may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 5. G.CO.11 theorems about parallelograms. Ability to construct a proof using one of Students will base this new learning on what they know about the relationships Theorems include: opposite sides are a variety of methods that exist between the angles formed when congruent, opposite angles are congruent, the parallel lines are cut by a transversal. diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Cluster Note: Build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.
Cluster Note: Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. G.CO.9 theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Note: This is an overarching standard that will be revisited throughout the course. See the skills and knowledge that are stated in the Standard. Students will base this new learning on what they know about : linear supplementary and complementary angles Parallel lines cut by a transversal This is an opportunity to also include same side interior (consecutive) angles and alternate exterior angles in the theorems from parallel G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Note: Implementation of this standard may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 5. Ability to construct a using one of a variety of methods G.CO.11 theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Ability to construct a proof using one of a variety of methods Students will base this new learning on what they know about the relationships that exist between the angles formed when parallel lines are cut by a transversal. Cluster Note: Build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.
Day_1_HS_Afternoon_Geometry_Unit_1.docx