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Download Subject Geometry Academic Grade 10 Unit # 2 Pacing 8
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Subject Geometry Academic Grade 10 Unit # 2 Pacing 8-10 weeks Triangles and Quadrilaterals Unit Name Overview In Unit 2 students will thoroughly study the properties of triangles. Students will be able to identify congruent triangles, write congruence statements, and apply theorems to prove triangles congruent. Students will also study the properties of quadrilaterals and be able to identify the different quadrilaterals by their sides and angles. The unit will also have students investigate properties of triangles and quadrilaterals on the coordinate plane. Students will identify figures and find perimeters using algebraic concepts. Standard # Standard MC, SC, or AC 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. G.CO.10 MC SLO # Student Learning Objectives Depth of Knowledge 1 2 3 4 5 6 7 8 9 Apply the Triangle Angle Sum Theorem Apply the Third Angle Theorem Apply the Exterior Angle Theorem Apply the Angle, Angle, Side Congruency Theorem Apply the Isosceles Triangle Theorem Apply the Converse of the Isosceles Triangle Theorem Apply the Triangle Midsegment Theorem Apply the Exterior Angle Inequality Theorem Apply the fact that the side opposite the greater angle in a triangle is longer than the side opposite the lesser angle, and the converse of these relationships Prove that the perpendicular segment from a point to a line is the shortest segment (distance) from the point to the line Apply the Triangle Inequality Theorem Apply the Side Angle Side Inequality Theorem Apply the Side, Side. Side Inequality Theorem 4 Apply rigid motion arguments to show that two triangles are congruent Apply rigid motion arguments to show that two geometric figures are congruent Prove two triangles congruent using the SSS Theorem 4 10 11 12 G.CO.7 G.CO.8 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent Explain how the criteria for triangle congruence 13 MC MC 14 15 4 16 17 18 19 20 (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle G.CO.11 Prove 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 SC MC 21 22 23 24 25 26 27 28 29 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures G.SRT.5 30 MC 31 G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2) 32 MC 33 34 35 G.GPE.7 Big Ideas Use coordinates to compute the perimeters of polygons and areas of triangles and rectangles (e.g using the distance formula) MC 36 Prove two triangles congruent using the SAS Theorem Prove two Triangles congruent using the ASA Theorem Prove two triangles congruent using the AAS Theorem Prove two triangles congruent using the HL Theorem Generate formal constructions of regular polygons inscribed in a circle with paper folding, geometric software or other geometric tools. Apply the following facts about parallelograms: Opposite sides of a parallelogram are congruent Opposite angles of a parallelogram are congruent The diagonals of a parallelogram bisect each other The diagonals of a rectangle are congruent The fact that the diagonals of a rhombus are perpendicular The diagonals of a rhombus bisect a pair of opposite angles A quadrilateral with any one of these properties is a parallelogram A quadrilateral has one pair of sides both parallel and congruent is a parallelogram Apply congruence and similarity criteria for triangles to solve problems Apply congruence and similarity criteria to prove relationships in geometric figures. Justify solutions to problems involving side lengths and angle measures using triangle congruence and similarity criteria Prove simple geometric theorems algebraically using the coordinates of vertices of polygons Calculate the perimeter and area of figures in the coordinate plane using the coordinates of the vertices of geometric figures Represent geometric figures on a coordinates plane Calculate the perimeter and area of figures in the coordinate plane using the coordinates of the vertices of the figures Represent geometric figures in the coordinate plane using the coordinates of the vertices of the figure 4 4 4 4 3 4 3 2 3 2 Properties of triangles Polygon and triangle congruence Polygon and triangle similarity Parallelograms Essential questions What combination of properties will make two triangles similar? What combination of properties will make two triangles congruent? What combination of properties will make a quadrilateral a parallelogram? Key Vocabulary Isosceles triangles, Equilateral triangles, Equiangular triangles, perpendicular bisector, congruent and similar triangles, similar and congruent triangles, quadrilateral, parallelogram Suggested Resources (list specific chapters and or page numbers from existing text that correspond to the SLOs and Standards) Chapter 4 Chapter 5 (Exclude section 5-4) Chapter 6