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Transcript
Advanced Geometry 2nd Semester Study Guide Unit 4: Triangle Congruence 4.1 Determine and justify that two triangles are congruent using congruence theorems What are congruent triangles? Use the definition of congruence in terms of rigid transformations to determine whether 2 figures are congruent and describe the sequence of rigid motions o Reflection, Rotation, Translation Write a congruence statement (order matters!) Determine if triangles are congruent (SSS, SAS, ASA, AAS Theorems) (Not SSA!!) o Other definitions/theorems that help: 4.2 Isosceles Triangle Defintion/Theorem Reflexive Property Midpoint Theorem Definition of Segment/Angle Bisector Parallel Line Theorems (AIA, Corresponding Angles, SSIA, AEA) Vertical Angle Theorem Definition of Equilateral Triangle Proofs! Solve Problems involving congruent triangles and corresponding parts Corresponding Parts of Congruent Triangles are Congruent (CPCTC) o When do we use it? (What must be shown first?) Use a congruence statement to match the corresponding parts of the triangles Proofs! Unit 5: Similarity 5.1 Identify similar triangles and use proportions and triangle properties to solve and justify solutions to problems What are similar triangles? o Angles are ______________ o Sides are _________________ Write a similarity statement (order matters!) Determine if triangles are similar (AA~, SSS~, SAS~) o Be sure to check to see if sides are proportional! Set up and solve proportions o Big triangle/little triangle o Triangle Proportionality Theorem o 3 parallel lines with 2 transversals o Angle bisector proportionality Triangle Midsegment Theorem o What is a midsegment? o How does it relate to the side of the triangle it doesn’t intersect 5.2 Determine and apply scale factor Find scale factor (of – top, to – bottom) o Enlargement: Scale Factor > ____ o Reduction: Scale Factor < ____ Dilations – What is it? o Find the center of dilation o Find the scale factor 5.3 Identify similar right triangles formed by the altitude drawn to the hypotenuse and use those properties to solve problems 𝑎 𝑥 Geometric Mean: 𝑥 = 𝑏, x is the geometric mean of a and b What is an altitude? A right triangle with an altitude drawn to the hypotenuse forms 3 similar triangles o Write a similarity statement for them o Write 3 different proportions Legs and altitude are geometric means Parts of the hypotenuse are the a and b Unit 6: Right Triangle Relationships and Trigonometry 6.1 Use Pythagorean Theorem to identify and justify relationships in triangles and apply relationships in problems involving right triangles Simplify square roots Pythagorean Theorem o What is it? o What must be true before you can use it? Special Right Triangles o 45-45-90: What is the rule? o 30-60-90: What are the rules? 6.2 Solve right triangles and application problems using trigonometric ratios Trig ratios: o How do you remember the pattern? o What do you use to find missing angles? Word problems: o Angles of elevation/depression: where are they? o Eye level problems: how does it affect the problem? Unit 7: Quadrilaterals 7.1 Solve application problems involving the properties of quadrilaterals How do you name quadrilaterals Sum of the angles of a quadrilateral: Study the family tree or table of characteristics Properties of Parallelograms: o o o o o Properties of Rectangles: (all properties of parallelograms +) o o Properties of Rhombi: (all properties of a parallelogram +) o o o Properties of Squares: Property of Trapezoids: o Isosceles Trapezoids: o Midsegment: Properties of Kites: o o o o o 7.2 Identify quadrilaterals on a coordinate plane, and justify the identification using the appropriate tools and methods Determine what type of quadrilateral is formed by 4 points o Slope Formula: How does it help? o Distance Formula: How does it help? o Midpoint Formula: How does it help? 4 ways to test for a parallelogram: 2 ways to test for a rectangle: 2 ways to test for a rhombus: Test for a trapezoid (isosceles?): If no parallel sides, how do you test for a kite: