Week 1 - Prince George's County Public Schools

Geometry Enrichment/Instructional Packet

Answer Key

Mathematics

Prince George’s County Public Schools Division of Academics

Department of Curriculum and Instruction

Week 1

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Resource: enVision Geometry Lesson: 3-1 Reflections, 3-2 Translations, 3-3 Reflections Objective: Identify transformations that preserve distance and angle, and compare them to those that do not. Describe translations, reflections, and rotations as functions that transform an input point to an output point. Draw the transformed figure given a figure and a transformation. Specify a sequence of transformations that will carry a figure onto another. Content Standards: G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

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MCAP

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Week 1 MCAP Practice Assessment Problems #1 B #2 Part A

Part B C

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Week 2

Resource: enVision Geometry Lesson: 4-3 Proving and Applying Congruence Criteria Objective: Use properties of rigid motions to prove that two triangles are congruent. Use transformations, along with congruence criteria for triangles, to prove relationships among triangles and solve problems. Content Standards: G.CO.7 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. G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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Week 2 MCAP

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Practice Assessment Problems

#1

#2 C, D, E, F #3

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Week 3

Resource: enVision Geometry Lesson: 2-2 Proving Lines Parallel Objective: Use given geometric theorems and properties of rigid motions, lines, angles, triangles and parallelograms to prove statements about angle measurement, triangles, distance, line properties and congruence and solve problems. Content Standards: G.CO.9 Prove 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.

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Week 3 MCAP

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Practice Assessment Problems

#1 Part A D Part B B #2 Part A D, E Part B C, E

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Week 4

Resource: enVision Geometry Lesson: 9-1 Polygons in the Coordinate Plane Objective: Use coordinates to prove simple geometric theorems algebraically. Use geometric relationships in the coordinate plane to solve problems involving area, perimeter of polygons, and ratios of lengths. Content Standards: 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. G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

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Week 4 MCAP

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Practice Assessment Problems

#1 Part A 70.6 Part B 68 #2

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Week 5

Resource: enVision Geometry Lesson: 7-2 Similarity Transformations Objective: Use similarity transformations to prove that two triangles are similar. Content Standards: G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

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Week 5 MCAP

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Practice Assessment Problems

#1 A, B, D, E #2

#3

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Week 6

Resource: enVision Geometry Lesson: 8-2 Trigonometric Ratios Objective: Use similarity transformations with right triangles to define trigonometric ratios for acute angles, and understand the relationship between sine and cosine. Use trigonometric ratios, the Pythagorean Theorem, and the relationship between sine and cosine to solve right triangles in applied problems. Content Standards: G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

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MCAP Practice Assessment Problems

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#1 A, D #2 B, D, G #3

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Extension

Resource: enVision Geometry Lesson: 10-2 Lines Tangent to a Circle Objective: Apply properties and theorems of angles and segments in circles to identify and describe relationships and solve problems. Content Standards: 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.

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MCAP Practice Assessment Problems

#1 B #2 Part A A, C, E Part B D