Question

Prove the indicated result of Proposition 35 in question #8 that pertains from Book 1 of Euclid’s Elements.

Step 1

Consider the given figure:

Step 2

Now, in triangle *ABC* and *DCF* :

*AB=CD* (since, ABCD is a parallelogram)

∠ABE = ∠DCF (since, ∠BAD= ∠CDF and Angle ∠AEB = angle ∠DFC)

*BE=CF* (since, *BEFC* is a parallelogram)

Thus, by SAS property:

*∆ABC* ≡ *∆DCF*

Step 3

Therefore,

*Ar *(*∆ABC*) = *Ar *(*∆DCF*)

*Ar *(*ABGD*)+* Ar *(*DGE*) = *Ar *(*EFCG*) +* Ar *(*DGE*)

*Ar *(*ABGD*) = *Ar *(*EFCG*)

Now, add the area of triangle *BGC* to both sides:

*Ar *(*ABGD*)+* Ar *(*BGC*) = *Ar *(*EFCG*) +* Ar *(*BGC*)

*Ar ***( ABCD) = Ar (BCF...**

Tagged in

Q: 1. Given a line P(t) through the points Po = [1,0|7 and P [2,4]7 in 2D (a) Extend P(t) to homogeneou...

A: Given a line p(t) through the points

Q: #8

A: From the given information:u, v , w are the three vectors in R3. So let,

Q: The product of three integers is −2. Determine all of the possible values for the three factors. Wri...

A: Let x, y and z be the three factors of the product –2.The possible values for the three factors are ...

Q: A weighted coin with Pr[H]=4/5 is flipped two times. What is the probability at least one of the fli...

A: From the given information:Probability of getting head when a weighted coin is flipped =4/5Probabili...

Q: Claim: For any natural number n, if 6 ∣ n, then 3 ∣ n.

A: Use the mathematical induction to show that the given statement “For any natural number n, if 6 ∣ n,...

Q: Problems, Section 9 number 8,10,11,13. Please answer the questions

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Escalate

A: The question is converned with linear operators, matrix representations and determinants

Q: Let m and n be positive integers with gcd(m,n) = 1. Prove that Z/mZ x _Z/ nZ = Z/mnZ

A: Suppose m and n are relatively prime.

Q: Is a permutation of one element considered to be an even permutation? For example, is (1) an even pe...

A: To clarify the notion of an even permutation

Sorry about that. What wasn’t helpful?