Honors :REVISITING THE PYTHAGOREAN THEOREM WITH SIMILARITY15In Lesson 2.3.2, you proved the Pythagorean Theorem using a proof involving thearea of triangles and squares. Did you know that you can also prove the PythagoreanTheorem using triangle similarity? For example, in triangle ABC with right angle atA below, how can similarity be used to prove that (AB) +(AC) (BC)? In thisproblem, you will support this proof by providing reasons for each part of thejustification.a. Find three different triangles in the diagram.Why are all of these triangles similar?Bb. 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)?

(A) Three different Δ are ΔABC, ΔADC , ΔADB all are similar.Because all are right angle Δ.…

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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Question

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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