Rotations, reflections, translations and congruency are developed experimentally in grade 8, and this experience is built upon in geometry, giving greater attention to precise definitions and formal reasoning. Properties of lines and angles, triangles and parallelograms were investigated in Grades 7 and 8. In geometry, these properties are revisited in a more formal setting, giving greater attention to precise statements of theorems and establishing these theorems by means of formal reasoning. In this quarter students develop the relationship between transformations and congruency. Students study congruence, namely experimenting with transformations in the plane, understanding congruence in terms of rigid motions, proving geometric theorems, prove geometric theorems, and make geometric constructions with a variety of tools. Students also use congruence and similarity criteria for triangles to solve problems and to prove relationships. Additionally, in this quarter, students use coordinates to prove simple geometric theorems algebraically.Formative and summative assessments are based upon lessons taught and student needs.
Standards G.CO.A.1, G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.CO.B.7, G.CO.C.9, G.CO.D.12, G. GPE.B.2, G. GPE.B.3
Quarter 2
Triangle Congruence with Applications Properties of Triangles Special Segments inTriangles Properties ofQuadrilaterals with Coordinate Proof
During the second quarter students continue to work with the concept of rigid motion and congruency. They will determine if two triangles are congruent by SSS, SAS, ASA, AAS, or HL and then provide appropriate reasoning for why they are congruent. They also gain a deeper insight into constructing two-column, paragraph,and coordinate proofs. Students classify triangles based on its’angles and side measures and determine whether a triangle exists given three side measures and find the range of the third side when given two side measures. Students compare the sides or angles of a given triangle and apply the Hinge theorem. Students learn how to find missing angles in triangles both interior and exterior angles. They investigate the special segments of a triangle; altitude, angle bisector, perpendicular bisector, and median. They also practice with the points of concurrency; orthocenter, incenter, circumcenter, and centroid. Identifying quadrilaterals using given properties concludes the second quarter. Students should be able to solve equations to find various missing parts of the quadrilaterals as wellFormative and summative assessments are based upon lessons taught and student needs.
Standards G.CO.B.7, G.CO.B.8, G.CO.C.10, G.CO.C.11, G.CO.D.12, G. SRT.B.4, G. SRT.B.5, G. GPE.B.2, G. GPE.B.5, G.MG.A.1, G.MG.A.2as write two-column, paragraph and coordinate proofs using definitions and properties.
Quarter 3
Similarity and Transformations Using Similar Triangles Right Triangles withTrigonometry Properties of Angles andSegments in Circles
44 Days
During the third quarter students formalize their understanding of similarity, which was informally studied prior to geometry. Similarity of polygons and triangles is explored and triangle similarity postulates and theorems are formally proven. The proportionality of corresponding sides of similar figures is applied. Similarity is extended to the side-splitting, proportional medians, altitudes, angle bisectors, and segments theorems. The geometric mean is defined and related to the arithmetic mean. The special right triangles of 30-60-90 and 45-45-90 are studied. Students are introduced to the right -triangle trigonometric ratios of sine, cosine, and tangent, and their applications. Angles and the sine, cosine, and tangent functions are defined in terms of a rotation of a point on the unit circle. Students end the quarter by starting their study of circles, reviewing circumference and identifying central angles, major and minor arcs, semicircles and find their measures. They end the quarter by studying inscribed angles and intercepted angles. Throughout students apply geometric concepts to modeling situations.Formative and summative assessments are based upon lessons taught and student needs.
Standards G.CO.A.1, G. SRT.A.1, G. SRT.A.2, G. SRT.A.3, G. SRT.B.4, G. SRT.B.5, G. SRT.C.6, G. SRT.C.7, G. SRT.C.8, G. MG.A.2, G. GMD.A.1, G.C.A.1, G.C.A.2
Quarter 4
Properties of Angles and Segments in Circles, Arc Length, Sector Area,and Equations of Circles Use Coordinates to ProveSimple GeometricTheorems Algebraically Volume of Solids, Visualizing Solids Trigonometry with AllTriangles
45 Days
During the fourth quarter students continue their study of circles. They explore and apply the properties of angles and segments in circles including the intersection of two secants, two tangents, two chords or a secant and a tangent. Then they find and apply arc length and area of sectors and write equations of circles and graph them in the coordinate plane. Students use coordinates to prove simple geometric theorems algebraically and then students explain volume formulas and use them to solve problems in prisms, pyramids, cylinders, cones and spheres. Students learn how to construct regular hexagons, squares, and triangles in circles. Additional content/standards that will be addressed after the TNReady assessment include extending their understanding of surface area of solids and continuing to apply geometric concepts in modeling situations. The year will conclude by studying law of sines and cosines to find missing sides in any triangle, not just right triangles.Formative and summative assessments are based upon lessons taught and student needs.
Standards G.CO.D.12, G.C.A.2, G.C.A.3, G.C.B.4, G. GPE.A.1, G. GPE.B.2, G. GPE.B.3, G. GPE.B.4, G.MG.A.1, G. MG.A.2, G. GMD.A.1, G. GMD.A.2