Which construction can you use to prove the Pythagorean Theorem based on similarity of triangles?
2 answers:
Answer: Draw perpendicular to the hypotenuse that goes through point of right angle.
Step-by-step explanation:
Let ΔABC be any triangle right angled at B, then a line segment perpendicular to AC (hypotenuse) and name it point D such that in ΔABC and ΔABD, ∠B=∠ADB =90° and ∠A=∠A (common in both triangles) ,therefore by AA similarity criteria ΔABC is similar to ΔABD....> which can be use to prove the Pythagoras theorem.
Pythagoras theorem states that in any right angled triangle the square of the longest side is equal to the sum of the square of other two sides.
The construction that you can use to prove the Pythagorean Theorem based on similarity of triangles is 2nd construction. Please see the attached file.
To add, in mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It mentions that the sum of the squares of the other two sides is equal to the square of the hypotenuse (the side opposite the right angle).
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We could write such a number as
so we're done.
Answer: Yes I agree, they must be identical to each other.
Step-by-step explanation: One of the conditions based on which triangles are similar is the SSA criteria, that is, Side-Side-Angle.
According to Tyler, two sides have been measured as 11 units and 8 units respectively in both triangles. If the corresponding angle is the same as indicated in the question, then the third side must be the same measurement. However, if the angles are of different sizes, then the third side would also be different for both triangles. For instance if the angle in triangle A is wider than that of triangle B, then the third side in triangle A would be longer than that of triangle B and in that case they would not be similar. Also if the angle in triangle A is narrower than that of triangle B, then the third side of triangle A would be shorter than that of triangle B and both triangles would not be similar as well.
Please refer to the picture attached. In the upper part of the picture, triangle A and triangle B are not similar though they both have sides measuring 11 and 8 units because angle x is not equal to angle y. However in the lower part, both triangles A and B are equal because both have angle x and sides 11 and 8 units, and that makes the third side have the same measurement.
