"Converse Theorem of Pythagorean Theorem" Pythagorean Theorem PPT courseware 4

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"Converse Theorem of Pythagorean Theorem" Pythagorean Theorem PPT courseware 4

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1. Draw: Draw a triangle whose side lengths are the following numbers (unit: centimeters)

A: 3, 4, 3; B: 3, 4, 5; C: 3, 4, 6; D: 6, 8, 10

2. Measure: Use your protractor to measure the maximum angle of each of the above triangles, and record it as follows: A: ____ B: ____ C: ____ D: ____

3. Judgment: Please judge the shape of the triangle you drew above.

A:______ B:_______ C:______ D______

4. Find the pattern: Based on the side lengths of each triangle given above, please find the relationship between the square of the longest side and the sum of the squares of the other two sides.

A: _____ B: _____ C: _____ D: ______

5. Conjecture: Let us guess what relationship the lengths of each side of a triangle should satisfy so that this triangle can be a right-angled triangle?

Your guess is_____________.

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

Known: In △ABC, AB=c BC=a CA=b

And a2+b2=c2

A long time ago, the ancient Egyptians tied a long rope with 13 knots at equal distances, and then nailed it with pegs to form a triangle as shown in the picture. Do you know what the shape of this triangle is? and explain the reasons.

Solution: This triangle is a right triangle.

Reason: Suppose the distance between the two knots is a, then the three sides are 3a, 4a, and 5a respectively.

∵(3a)²+(4a)²=(5a)²

∴The triangle is a right triangle

If the three sides of △ABC are a, b, and c respectively and satisfy

a2＋b2＋c2+50＝6a＋8b+10c,

Determine the shape of △ABC.

This triangle is a right 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: 2024-11-18

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