Can someone please help me with this ASAP
1 answer:
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Answer:
Look at the picture. The answer and the steps are all in it.
Pythagorean Theorem: a^2 + b^2 = c^2
-A and B are legs of the triangle
-C is the hypotenuse
#1.
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
c = 10
#2.
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
c = 13
#4.
10^2 + 4^2 = c^2
100 + 16 = c^2
116 = c^2
c =
#5.
15^2 + 9^2 = c^2
225 + 81 = c^2
306 = c^2
c =
#6.
120^2 + b^2 = 150^2
14400 + b^2 = 22500
b^2 = 8100
b = 90
#7.
144^2 + b^2 = 194^2
20736 + b^2 = 37636
b^2 = 16900
b = 130
Hope this helps!! :)
Answer: Pythagorean Theorem Pieces of Right Triangles is not a justification for the proof.
Explanation : Here, is a right triangle with sides a, b and c. Perpendicular CD forms right triangles BDC and CDA.
CD measures h units, BD measures y units, DA measures x units.
Draw an altitude from point C to Line segment AB Let segment BC = a segment CA = b, segment AB = c, segment CD = h, segment DB = y, segment AD = x,
y + x = c
a/c=y/a( Similarity theorem in triangles ABC and DBC )
------(1) (Cross Product Property)
Similarly, (Similarity theorem in triangles ABC and ADC)---------(2)
(after adding equation (1) and (2) )
( By additional property of equality)
. ( because y + x=c)
Thus, it has been proved that except Pythagorean Theorem Pieces of Right Triangles we use all other properties.