Geometry, Teacher\'s Edition

(Axel Boer) #1

Converse of the Pythagorean Theorem


I.SectionObjectives



  • Understand the converse of the Pythagorean Theorem.

  • Identify acute triangles from side measures.

  • Identify obtuse triangles from side measures.

  • Classify triangles in a number of different ways.


II.ProblemSolvingActivity-FigureThoseTriangles



  • This is a game that has the students use number cards to figure out whether triangles are right triangles, acute
    triangles or obtuse triangles.

  • To prepare for this game, use index cards and write one number on each card. Number the cards 2−25. Each
    group will need a set of cards to play the game.

  • Divide the students into groups.

  • Students are going to use the number cards to create as many different types of triangles as they can.

  • Begin with right triangles.

  • Students are given a short period of time to use the number cards to create as many different combinations of
    numbers that will equal right triangles. For example, using 3− 4 −5, the students will have a right triangle
    because 3^2 + 42 = 52.

  • Students work together to write out as many as possible using the numbers 2− 25.

  • Then move on to acute triangles. Remind students thata^2 +b^2 >c^2.

  • Then move on to obtuse triangles. Remind students thata^2 +b^2 <c^2.

  • Finally have students share their combinations.

  • Winning teams can be determined based on the number of combinations created and on accuracy.


III.MeetingObjectives



  • Students will use number combinations to determine side lengths of right triangles.

  • Students will use number combinations to determine side lengths of acute triangles.

  • Students will use number combinations to determine side lengths of obtuse triangles.


IV.NotesonAssessment



  • Walk around as students play the game.

  • Offer assistance when needed.

  • Have students share their combinations to determine accuracy.


Using Similar Right Triangles


I.SectionObjectives



  • Identify similar triangles inscribed in a larger triangle.

  • Evaluate the geometric mean of various objects.

  • Identify the length of an altitude using the geometric mean of a separated hypotenuse.

  • Identify the length of a leg using the geometric mean of a separated hypotenuse.


Chapter 5. Geometry TE - Problem Solving
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