Honors : REVISITING THE PYTHAGOREAN THEOREM WITH SIMILARITY 15 In Lesson 2.3.2. you proved the Pythagorean Theorem using a proof involving the area of triangles and squares. Did you know that you can also prove the Pythagorean Theorem using triangle similarity? For example, in triangle ABC with right angle at A below, how can similarity be used to prove that (AB) +(AC)² = (BC) ? In this problem, you will support this proof by providing reasons for each part of the justification. a. Find three different triangles in the diagram. Why are all of these triangles similar? B b. Carol argues that and -16. Do you agree? Why or why not? How can you use Carol's equations to show that (AB) -(CBXDB) and (AC) = (BCXDC)? d. Why does (AB) +(AC) (CBXDB)+(BCX(DC)? e. Why does (CB(DB)+(BCXDC)= BC(DB+ DC)= (BC)?? f. Finish the proof: Why does (ABY +(ACy? = (BC) ?
Honors : REVISITING THE PYTHAGOREAN THEOREM WITH SIMILARITY 15 In Lesson 2.3.2. you proved the Pythagorean Theorem using a proof involving the area of triangles and squares. Did you know that you can also prove the Pythagorean Theorem using triangle similarity? For example, in triangle ABC with right angle at A below, how can similarity be used to prove that (AB) +(AC)² = (BC) ? In this problem, you will support this proof by providing reasons for each part of the justification. a. Find three different triangles in the diagram. Why are all of these triangles similar? B b. Carol argues that and -16. Do you agree? Why or why not? How can you use Carol's equations to show that (AB) -(CBXDB) and (AC) = (BCXDC)? d. Why does (AB) +(AC) (CBXDB)+(BCX(DC)? e. Why does (CB(DB)+(BCXDC)= BC(DB+ DC)= (BC)?? f. Finish the proof: Why does (ABY +(ACy? = (BC) ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Honors :
REVISITING THE PYTHAGOREAN THEOREM WITH SIMILARITY
15
In Lesson 2.3.2, you proved the Pythagorean Theorem using a proof involving the
area of triangles and squares. Did you know that you can also prove the Pythagorean
Theorem using triangle similarity? For example, in triangle ABC with right angle at
A below, how can similarity be used to prove that (AB) +(AC) (BC)? In this
problem, you will support this proof by providing reasons for each part of the
justification.
a. Find three different triangles in the diagram.
Why are all of these triangles similar?
B
b. Carol argues that and E= E. Do you agree? Why or why not?
How can you use Carol's equations to show that (AB)? = (CBX(DB) and
(AC) = (BCXDC)?
d. Why does (AB)+(AC)=(CBXDB)+(BCXDC)?
e. Why does (CB)(DB)+(BCXDC)= BC(DB+ DC)= (BC)²?
f. Finish the proof: Why does (ABY +(ACy =(BC)?
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