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Given:

ABC is a right triangle, with a right angle at ∠C

Prove:

a^2 + b^2 = c^2

 

Image:

https://prnt.sc/i58fyf

 

 

 

 

Statement

Reason

1.   ABC is a right triangle, with a right angle
at ∠C

1. Given

2.   Draw an altitude from point C to AB.

2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.

3.   CDB and CDA are right angles.

3. Definition of altitude

4.   ∠BCA ≅ ∠BDC

All right angles are congruent.

5.   ∠B ≅ ∠B

 XXX

6.   XXX

AA Similarity Postulate

7.   a/x = c/a

 XXX

8.   a^2 = cx

 XXX

9.   ∠CDA ≅ ∠BCA

 XXX

10.  ∠A ≅ ∠A

 XXX

11.  XXX

AA Similarity Postulate

12.  b/y = c/b =

 XXX

13.  b^2 = cy

 XXX

14.  a^2 + b^2 = cx + cy

 XXX

15.  XXX

Distributive Property

16.  x+y=c

 XXX

17.  a^2 + b^2 = c^2

 XXX

Guest Jan 25, 2018
 #1
avatar+86915 
+1

See if this helps  :

 

https://web2.0calc.com/questions/please-check-my-geometry-proof-they-hate-me

 

 

cool cool cool

CPhill  Jan 25, 2018

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