"The Converse Theorem of the Pythagorean Theorem" PPT Courseware 3 of the Pythagorean Theorem

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"The Converse Theorem of the Pythagorean Theorem" PPT Courseware 3 of the Pythagorean Theorem

The converse of the Pythagorean theorem

If the side lengths a, b, and c of a triangle satisfy a2 + b2 = c2, then the triangle is a right triangle. And the angle subtended by side c is a right angle.

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

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 _____ _____ ;

Three positive integers that can become the lengths of the three sides of a right triangle are called Pythagorean numbers.

Theorem and Converse Theorem

If the converse of a theorem is proved to be true,

Then it is a theorem. These two theorems are called reciprocity theorems.

One of the theorems is called the converse of the other.

We have already learned some reciprocal theorems, such as:

Pythagorean theorem and its converse,

If two straight lines are parallel, the angles of the same angles are equal; if the angles of the same angles are equal, the two straight lines are parallel.

group discussion

1. If line segments a, b, c can form a right triangle, their ratio may be ( )

A. 3:4:7; B. 5:12:13; C. 1:2:4; D. 1:3:5.

2. If the lengths of the three sides of a right triangle are expanded by the same multiple, the resulting triangle is ( )

A. It is a right triangle; B. It may be an acute triangle;

C. It may be an obtuse triangle; D. It cannot be a right triangle.

3. The three sides of the triangle are a, b, c, and satisfy the equation (a+b)2-c2=2ab, then the triangle is: ( )

A. Right triangle; B. Acute triangle;

C. Obtuse triangle; D. Isosceles right triangle.

4. It is known that BC=41, AC=40, AB=9 in ΔABC, then this triangle is a _______ triangle, and ______ is the largest angle.

5. Take the three sides of ΔABC as side lengths and draw a square outward. The areas obtained are 25, 144, and 169. Then this triangle is a ______ triangle.

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For more information about the PPT courseware "The Pythagorean Theorem and the Converse Theorem of the Pythagorean Theorem", please click the Pythagorean Theorem ppt The Converse Theorem of the Pythagorean Theorem ppt tag.

"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: 2024-11-23

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