protractor, tracing paper, scissors, disprove that a figure defined by four tape. given points in the coordinate plane is a rectangle; prove or disprove that the Geometer’s Sketchpad or point (1, ) lies on the circle centered at software. the origin and containing the point (0, Geogebra Software 2). G.GPE.5. Prove the slope criteria for 3.5 Equations of Parallel and parallel and perpendicular lines and Perpendicular Lines Mathematics Vision Project use them to solve geometric problems 8.3 Proving Triangle Similarity by (e.g., find the equation of a line SSS and SAS parallel or perpendicular to a given Mars Task: line that passes through a given point). G.GPE.6. Find the on a directed 3.5 Equations of Parallel and line segment between two given points Perpendicular Lines that partitions the segment in a given 8.4 Proportionality Theorems ratio. Use coordinates to compute 1.4 Perimeter and Area in the G.GPE.7. perimeters of polygons and areas of Coordinate Plane triangles and rectangles, e.g., using the distance formula. ★ Understand and apply theorems Geometry - Circles 10.2 Finding Arc Measures Illustrative Mathematics about circles G.C.1. Prove that all circles are similar. 10.1 Lines and segments That G.C.2. Identify and describe Intersect Circles relationships among inscribed angles, 10.2 Finding Arc Measures radii, and chords. 10.3 Using Chords Include the 10.4 Inscribed Angles and Polygons relationship between central, Mars Find arc lengths and areas of sectors 10.5 Angle Relationships in Circles inscribed, and circumscribed angles; of circles 10.6 Segment Relationships in Circles inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Inside Mathematics: G.C.3. Construct the inscribed and 6.2 Bisectors of Triangles circumscribed circles of a triangle, and 10.4 Inscribed Angles and Polygons prove properties of angles for a quadrilateral inscribed in a circle.
disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ) lies on the circle centered at the origin and containing the point (0, 2). G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G.GPE.6. Find the on a directed line segment between two given points that partitions the segment in a given ratio. G.GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. ★ 3.5 Equations of Parallel and Perpendicular Lines 8.3 Proving Triangle Similarity by SSS and SAS 3.5 Equations of Parallel and Perpendicular Lines 8.4 Proportionality Theorems 1.4 Perimeter and Area in the Coordinate Plane protractor, tracing paper, scissors, tape. Geometer’s Sketchpad or software. Geogebra Software Mathematics Vision Project Mars Task: Understand and apply theorems about circles Find arc lengths and areas of sectors of circles Geometry - Circles G.C.1. Prove that all circles are similar. G.C.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G.C.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 10.2 Finding Arc Measures 10.1 Lines and segments That Intersect Circles 10.2 Finding Arc Measures 10.3 Using Chords 10.4 Inscribed Angles and Polygons 10.5 Angle Relationships in Circles 10.6 Segment Relationships in Circles 6.2 Bisectors of Triangles 10.4 Inscribed Angles and Polygons Illustrative Mathematics Mars Inside Mathematics: