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Geometry Drill

Geometry Drill. SAT: In the figure, j//k & l//m. If x+y =140, find the value of w. w o. l. y o. x o. m. j. k. Objective.

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Geometry Drill

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  1. Geometry Drill • SAT: In the figure, j//k & l//m. If x+y=140, find the value of w wo l yo xo m j k

  2. Objective • S.W. learn the triangle inequality theorem so that they can determine whether triangles of certain side lengths exist and find the relationship between the sides and angles of a triangle

  3. Triangle Inequality Postulate • The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  4. Could this a be Triangle? 7 15 6

  5. Could this be a Triangle? 12 7 5

  6. Conclusion • The largest side of a triangle is opposite the largest angle. • The shortest angle of a triangle is opposite the shortest side.

  7. Do you remember? What is the definition of an isosceles triangle?

  8. Q P ISOSCELES TRIANGLEvocabulary • legs • vertex angle • base • base angles Y

  9. Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite those sides are congruent. C B A

  10. ??????????????????????? Is the converse true?

  11. Converse Isosceles Triangle Theorem • If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

  12. ???????? • What if I bisect the vertex angle, what can you tell me? x 70º

  13. ???????? Find base 3x + 3 x2 – 1 9 – x

  14. ???????? x 70º

  15. ???????? • Find the missing angles x 70º

  16. Objective: To determine ways to prove triangles congruent

  17. Vocabulary • Congruent Polygons-Two polygons are congruent if and only if their vertices can be matched up so that corresponding sides and angles are congruent.

  18. Helpful Hint Two vertices that are the endpoints of a side are called consecutive vertices. For example, P and Q are consecutive vertices.

  19. To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS. In a congruence statement, the order of the vertices indicates the corresponding parts.

  20. Helpful Hint When you write a statement such as ABCDEF, you are also stating which parts are congruent.

  21. Congruent figures-diagram • Name the congruent triangles • ∆CAT ∆DOG G A D O C T

  22. DO OG DG D O G CA AT CT C A T SINCE, ∆CAT  ∆DOG Corresponding parts are .......

  23. CA & AR  R & C IS INCLUDED BETWEEN ____ & ____ RC IS INCLUDED BETWEEN ____ & _____ A R C INCLUDED??????

  24. POSTULATE - SSS POST. • If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.

  25. POSTULATE - SAS POST. • If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent.

  26. POSTULATE - ASA POST. • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent.

  27. To determine if triangles are congruent, what would you have to measure? • SSS • SAS • ASA • All sides & all angles.

  28. Which postulate, if any, can be used to prove the triangles congruent? 1. 2.

  29. 4.

  30. PROVE • GIVEN: line j | k • ∆ABC ∆FBE E A j k B C F

  31. Given: AB || DC; DC  ABProve: ∆ABC  ∆ CDA D C A B

  32. Statement AC  AC < BAC  _______ ∆ABC  ∆CDA Reason Given ____________ If_________ ____________ ____________ Proof

  33. Given: RS ST; TU ST; V is the midpoint of STProve: ∆RSV  ∆ UTV R S V U T

  34. Statement Reason Proof

  35. AAS THEOREM If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle then the triangles are congruent.

  36. Place HW on the corner of your desk 2 Column Proof Given Prove R T E P M

  37. STATEMENT 1. REASON 1. Given R E T P M

  38. Write down the name of the figure described. Only 1 figure. I will keep giving hints Hint 1 : I am a special polygon Hint 2: I have three sides Hint 3: I have an angle that is neither obtuse or acute Hint 4: My sides have a special relationship Right Triangle

  39. GT Geometry Given: Prove: E A D F B C

  40. Statement Reason

  41. HYPOTENUSE  LEGS D IS A RIGHT ANGLE FE IS CALLED THE ___?_______ DF & DE ARE CALLED ____?____ VOCABULARY D E F

  42. Pythagorean Theorem c b a

  43. Pythagorean Theorem a2 + b2 = c2 c b a

  44. HLTHEOREM If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle , then the triangles are congruent.

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