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The Converse of the Pythagorean Theorem

The Converse of the Pythagorean Theorem. What is the converse of a theorem?. If a theorem is p q (if p then q). The converse of that theorem is qp (if q then p). IF. A triangle has sides a,b, and c such that a 2 +b 2 =c 2. THEN. It is a right triangle.

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The Converse of the Pythagorean Theorem

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  1. The Converse of the Pythagorean Theorem

  2. What is the converse of a theorem? If a theorem is pq (if p then q) The converse of that theorem is qp (if q then p)

  3. IF A triangle has sides a,b, and c such that a2+b2=c2 THEN It is a right triangle So what is the converse of the Pythagorean Theorem?

  4. Practice 4 m 5 m 11 cm 6 cm 5 cm 8 cm These figures are not drawn accurately. Which of the triangles are right triangles

  5. You Do: 6 cm 8 cm 6 cm 5 cm 10 cm 4 cm 2 cm 7 cm 12 cm These figures are not drawn accurately, which of these triangles are right?

  6. Applications Pythagorean Theorem

  7. A ladder leans against a house. The feet of the ladder are 2.1 m from the base of the wall. The top of the ladder hits the house 3.8 m above the ground. How long is the ladder? 3.8 m x m 2.1 m Practice Together

  8. You Do: A rectangular gate is 3 m wide and has a 3.5 m diagonal. How high is the gate? 3 m 3.5 m x m

  9. A surveyor makes the following measurements of a field. Calculate the perimeter of the field to the nearest metre. 8 m 11 m 3 m 11 m 17 m Practice Together

  10. You Do: Satomi says she has just cut out a triangular sail for her boat. The lengths of the sides are 6.23 m, 3.87 m and 4.88 m. The sail is supposed to be right angled. Is it?

  11. Circle Problems: Chord of a Circle The line drawn from the centre of a circle at right angles to a chord bisects the chord. centre radius chord

  12. Practice Together Circle Problem: Chord of a Circle A chord of length 8 cm is 4 cm from the centre of a circle. Find the length of the circle’s radius

  13. You Do: Circle Problem: Chord of a Circle A chord of a circle has length 2 cm and the circle has radius 3 cm. Find the shortest distance from the centre of the circle to the chord.

  14. Circle Problems: Tangent-Radius Property A tangent to a circle and a radius at the point of contact meet at right angles centre radius point of contact tangent

  15. Circle Problem: Tangent-Radius Property If the earth has a radius of 6400 km and you are in a rocket 50 km directly above the earth’s surface, determine the distance to the horizon. 50 km Practice Together: Distance in the horizon 6400 km 6400 km

  16. Circle Problem: Tangent-Radius Property A circle has radius 2 cm. A tangent is drawn to the circle from point P, which is 9 cm from O, the circle’s centre. How long is the tangent? O 9 cm 2 cm You Do: P

  17. Three-Dimensional Problems Find the length of the longest nail that could be put entirely within a cylindrical can of radius 3 cm and height 10 cm. 3 cm 10 cm Practice Together:

  18. Three-Dimensional Problem A room is 6 m by 5 m and has a height of 3 m. Find the distance from a corner point on the floor to the opposite corner of the building 3 m 5 m 6 m You Do:

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