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Geometry Notes 6.9 ο· Name:_______________________________________ Period:____ I can use the distance formula and slope formula to prove or disprove a figure is s type of quadrilateral. G.GPE.4 Error Analysis Find the error(s) if any in each of the following examples. Be able to explain how to fix it or how you would have solved the problem correctly. Example One- Example Two- Example ThreeA Pizza Hut building is made up of several isosceles trapezoids. Prove that base angles of the roof are congruent. Statements Reasons 1) PIZA is an isosceles trapezoid 1) Given 2) Draw in ππ and π΄πΌ 2) Any two points determine a line segment 3) ππ β π΄πΌ 4) β πΌπ΄π β β πππ΄ 3) The diagonals of an isosceles trapezoid are congruent. 4) If lines are parallel, then alternate interior angles are congruent. 5) π΄π β π΄π 6) βπππ΄ β βπΌπ΄π 7) β ππ΄π β β πΌππ΄ (bases angles) 5) Reflexive 6) SAS 7) CPCTC Example Four- A The kite at right is a mathematically correct kite. Explain in sentences using words that the diagonals meet at right angles. M D By definition, a kite has adjacent sides congruent so Μ Μ Μ Μ Μ π΄π΅ β Μ Μ Μ Μ π΄π· . By the reflexive property Μ Μ Μ Μ Μ π΄π β Μ Μ Μ Μ Μ π΄π. By HL, βπ΄ππ· β βπ΄ππ΅ which means the diagonals of the kite must meet at right angles. C B Geometry Homework 6.9 Name:________________________________________ Period:____ Algebra Find the value(s) of the variable(s) in each isosceles trapezoid. 7. 8. 9. Find the measures of the numbered angles in each kite. 10. 11. 13. 14. Over 12. Find the measure of the numbered angles for each parallelogram. 1. 2. 3. 4. What is the precise name of a quadrilateral with vertices ? Find the values of the variables for which each figure is a parallelogram. 5. 6. Find the values of the variables. 1. 2. 3. In Exercises 4 and 5, decide whether the statement is true or false. If true, explain why. If false, show a counterexample. 4. A quadrilateral with congruent and perpendicular diagonals is a square or rhombus. 5. The diagonals of a kite separate the quadrilateral into four congruent triangles.