"The Converse Theorem of the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 2

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"The Converse Theorem of the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 2

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The following three sets of numbers are the side lengths a, b, and c of a triangle:

2.5, 6, 6.5; 6, 8, 10.

(1) Do these three sets of numbers satisfy a²+b²=c²?

(2) Draw the figures. Are they all right triangles?

What did you discover from the above examples? Please express your opinions in the form of propositions!

If the lengths of the three sides a, b, and c of a triangle satisfy a²+b²=c², then the triangle is a right triangle.

If the two right-angled sides of a right triangle are a and b, and the hypotenuse is c, then a²+b²=c²

If the converse of a theorem is proved to be true, then it is a theorem. These two theorems are called reciprocal theorems, and one of them is called the converse of the other theorem.

We have already learned some reciprocal theorems, such as:

Pythagorean theorem and its converse;

If two straight lines are parallel, the internal offset angles are equal; if the internal offset angles are equal, the two straight lines are parallel.

Is the triangle below with sides a, b, and c a right triangle? If so then which angle is a right angle?

(1) a=25 b=20 c=15 ____ _____ ;

(2) a=13 b=14 c=15 ____ _____ ;

(3) a=1 b=2 c=√3 ____ _____;

(4) a:b: c=3:4:5 _____ _____ ;

Like 25, 20, and 15, three positive integers that can become the lengths of the three sides of a right triangle are called Pythagorean numbers.

Independent evaluation:

1. The converse of the Pythagorean theorem

2. What are reciprocal propositions, original propositions and converse propositions?

3. What is called the mutual inverse theorem.

The converse of the Pythagorean theorem

If the square of the longer side of a triangle is equal to the sum of the squares of the other two shorter sides, then the triangle is a right triangle.

Known: In △ABC, AB=c BC=a CA=b and a2+b2=c2

Prove: △ ABC is a right triangle

Proof: Draw a △A’B’C’ so that ∠ C’=900, B’C’=a, C’A’=b

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"The Converse Theorem of the Pythagorean Theorem" PPT courseware 3:

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 3 1. Knowledge connection: Question 1. Can you tell what are the characteristics of a right triangle? (1) One angle is a right angle: (2) The right-angled side of 30 degrees is equal to the slope Half of the side; (3) Pythagorean Theorem: The sum of the squares of two right-angled sides is equal to the hypotenuse..

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 2:

"The Converse Theorem of the Pythagorean Theorem" PPT Courseware 2 Review the past and learn the new 1. Explain the Pythagorean Theorem in written language. The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse. 2. State its converse proposition and determine whether its converse proposition is true or false? if..

"The Converse Theorem of the Pythagorean Theorem" PPT courseware:

"The Converse Theorem of the Pythagorean Theorem" PPT courseware Review the past and learn the new 1. Explain the Pythagorean Theorem in written language. The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse. 2. State its converse proposition and determine whether its converse proposition is true or false? If three...

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Update Time: 2024-11-20

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