Given triangle(ABC) with A-D-C, then BD < BA or BD < BC. Prove that the set...

Given triangle(ABC) with A-D-C, then BD < BA or BD < BC.
Prove that the set consisting of a circle and its interior is a convex set.

Expert Solution

Colby Messinger answered 1 year ago

Suppose ABA′ holds(B is between A and A') and D ∈ Int(∠ABC). Prove that C ∈ Int(∠A′BD)....

Suppose A*B*A′ holds(B is between A and A') and D ∈ Int(∠ABC). Prove that C ∈ Int(∠A′BD). (a) Prove that C ∈ H(D,line A′B). (b) Prove that C ∈ H (A′, line←→BD). Use point A. (c) Deduce that C∈Int (∠A′BD).

Question: Prove the following: Claim: Consider a triangle ▵ABC and a point D on the interior...

Question: Prove the following: Claim: Consider a triangle ▵ABC and a point D on the interior of segment BC. If σ(▵ABC) = 180, then σ(▵ABD) = σ(▵ACD) = 180. Hint: Use the Split Triangle Theorem and/or the Split Quadrilateral Theorem

=>Set of functional dependencies(F) = {A -> BC, BC -> AD, D -> E} =>Set of...

=>Set of functional dependencies(F) = {A -> BC, BC -> AD, D -> E} =>Set of functional dependencies(F) = {AB -> C, A -> DE, B -> F, F -> GH, D -> IJ} Decompose the previous R{A, B, C, D, E, F, G, H, I, J} into each higher normal form relations above its current NF. For example, if its current NF is 0NF, then you need to decompose R to 1NF relations, 2NF relations, up to 3NF relations...

Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent...

Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent to DE, BC is congruent to EF, and AC is congruent to DF, then triangle ABC is congruent to triangle DEF. (Hint:Use three congruence axioms to reduce to the case where A=D, C=F, and points B and E are on opposite sides of line AC.)

Prove algebraically ABC+A’C’D’+A’BD’+ACD=(A’+C)(A+D’)(B+C’+D)

For triangle ABC, the lines: - through A, parallel to BC; - through B, parallel to...

For triangle ABC, the lines: - through A, parallel to BC; - through B, parallel to AC; - through C, parallel to AB intersect to form a triangle. Prove that the triangle is similar to triangle ABC.

ABC is a right triangle. AM is perpendicular to BC. The size of the angle ABC is equal to 55 degrees.

ABC is a right triangle. AM is perpendicular to BC. The size of the angle ABC is equal to 55 degrees. Find the size of angle ACM.

Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a...

Prove that the set R ={ a+ b√2+c√3+d√6 , a,b,c,d belongs to Q } is a field

Given ABC and ACD, prove the corollary to Axion B-4.

Given A*B*C and A*C*D, prove the corollary to Axion B-4.

Suppose that ac + bd = 0. Show that vectors [a, b] and [c, d] are...

Suppose that ac + bd = 0. Show that vectors [a, b] and [c, d] are perpendicular. The number ac + bd is called the dot product of the vectors [a, b] and [c, d].

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