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