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Ch. 3 Review Honors Geometry CCHS Transformations Topics Find image given a description of a translation, reflection, or rotation. Find image given a function describing a transformation. Determine if the transformation is a translation, reflection, rotation, or none of the above. Translate figures using directed line segments. Transformations Topics Reflect over a given line. Rotate 90 degrees or 180 degrees around a given point. Determine lines of reflectional symmetry. Understand the concept of rotational symmetry. Triangle Congruence Determine if triangles can be proved congruent by SSS, SAS, ASA, or none of the above. Write basic two-column proofs proving triangles congruent (MAKE SURE TO INCLUDE THREE CONGRUENCE STATEMENTS!) Apply properties to prove corresponding parts of triangles congruent. Transformations Give the image if the point (-1, 5) is translated up 2 and to the left 3. Give the image if (-3, 6) is reflected over the y axis. Give the image if (-2, 5) is reflected over the line y = 2. Transformations Give the image if (2, -5) is rotated 90 degrees clockwise about the origin. Give the resulting image if the function (x, y) (y, -x) is applied to the point (-1, 4). Is this a translation, reflection, or rotation? Write a function that reflects a point over the x-axis. Transformations Transformations How many lines of reflectional symmetry does the figure have? What is the smallest angle about which the pentagon has rotational symmetry? Which rule proves the triangles congruent? Given: 𝐴𝐶 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐵𝐴𝐷 𝐴𝐶 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠BCD ASA What rule proves the triangles congruent? SAS What rule proves the triangles congruent? Not enough information (SSA labeling) What rule proves the triangles congruent? Given: 𝑨𝑩 ≅ 𝑩𝑪 𝑩𝑫 𝒃𝒊𝒔𝒆𝒄𝒕𝒔 < 𝑨𝑩𝑪 SAS What rule proves the triangles congruent? Not enough information (AAS labeling) What rule proves the triangles congruent? Given: < 𝑾 ≅< 𝑲 𝑾𝑽 ≅ 𝑽𝑲 ASA One Step Proof: Given: < 𝑍𝑊𝑋 ≅< 𝑋𝑌𝑍 < 𝑋𝑊𝑌 ≅< 𝑍𝑌𝑊 Prove: < 𝑍𝑊𝑌 ≅< 𝑋𝑌𝑊 Subtraction Property One Step Proof Given: <1 comp. <4 <2 comp. <3 < 𝟏 ≅< 𝟐 Prove: < 3 ≅< 4 If angles are complementary to congruent angles, then they are congruent One Step Proof Given: 𝑊𝑌 ≅ 𝑋𝑍 Prove: WX ≅ YZ Subtraction Property One Step Proof: Given: 𝐷𝑀 ≅ 𝑁𝐹 M and N are mdpts Prove: DG ≅ FG Multiplication Property Chapter 3 Tips Labeling Congruent Triangles: Follow around the perimeter of a labeled triangle Review Properties (sec. 2.4-2.7 in book) Proofs: LABEL DIAGRAMS!!! Proofs: Include all labeling steps in proof Triangle Congruence Proofs: Make sure you have THREE CONGRUENCE statements! (Label S and A) Proofs: Make sure you have satisfied requirements of IF statements before including a step.