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Alisiya [41]
3 years ago
12

Which construction can you use to prove the Pythagorean Theorem based on similarity of triangles?

Mathematics
2 answers:
natima [27]3 years ago
6 0

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.

Rashid [163]3 years ago
4 0

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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A semicircle is drawn next to the base of an isosceles triangle such that its diameter is perpendicular to the triangle's
irina1246 [14]

The total area of the semicircle and triangle is 30 + 4.5π .

The diameter of the semicircle is perpendicular to the base of the triangle.

Given diameter length = 6 cm

radius = 6 /2 = 3cm

Area of the semicircle = 1/2 πr² = 1/2π3² = 4.5π

height of the triangle = 10 cm

Area of the triangle = 1/2 × 6 × 10 =30cm

Total area of the figure = 30 + 4.5π

hence the total area of the resulting figure is 30 + 4.5π

A semicircle with one locus of points is referred to as a half-circle in mathematics, more specifically geometry. A semicircle's complete arc is always equal to 180 degrees, radians, or a half-turn.

It only contains one reflectional symmetry line. A half-disk, a twofold geometric entity that includes both the circumferential segment from one end of the arc towards the other and all the inner points, is typically referred to as a "semicircle" in non-technical language.

Disclaimer: The complete question is :

A semicircle is drawn next to the base of an isosceles triangle such that its diameter of 6 cm is perpendicular to the triangle's altitude of 10 cm

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7 0
1 year ago
5 -2 (4a + 1) + 3a = 13 what is (a) equal to a) - 6/5 b) - 2 c) 2 d) 6/5
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3 years ago
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5q + 3 = 3h solving for q
lapo4ka [179]

Answer:

Im not sure tbh, but go to this website called Symbolab, and just type it in and it gives you a step by step process om how to solve it! ( :

Step-by-step explanation:

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3 years ago
The parabola below is a graph of the equation, -y+x=-4. Which of the points satisfy the inequality, -y+x ≤ -4 ? Check all that a
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3 years ago
If the fourth of 5 consecutive numebrs is 15, what is their sum?
Tju [1.3M]

BRAINLIEST PLEASEEEEEEEEEEEEE

Answer:

70

Step-by-step explanation:

You know the fourth number in this pattern is 15, and that they are all consecutive. With this information you know that the fifth number will be 16, and by counting backwards from 15 you can figure out all of the numbers are 12, 13, 14, 15, and 16. Now, to find the sum of these numbers you must add them together.

This is what it could look like: 12+13+14+15+16

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