Given: ΔABC Prove: The sum of the interior angle measures of ΔABC is 180°.

Statement

Reason

1. Let points A, B, and C form a
triangle.

given

2. Let be a line passing
through B, parallel to ,
with angles as labeled.

defining a parallel line and labeling angles

3.

4. m∠1 = m∠4, and
m∠3 = m∠5.

Congruent angles have equal measures.

5. m∠4 + m∠2 + m∠5 = 180°

angle addition and definition of a straight angle

6. m∠1 + m∠2 + m∠3 = 180°

substitution

What is the missing step in this proof?

A.
Statement: ∠4 ≅ ∠5, and ∠1 ≅ ∠3.
Reason: Alternate Interior Angles Theorem

B.
Statement: is parallel to .

Reason: is a transversal cutting and .

C.
Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.

Reason: Alternate Interior Angles Theorem

D.
Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.
Reason: ∠1 and ∠4, and ∠3 and ∠5 are pairs of supplementary angles.

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

number one is the correct answer

step-by-step explanation: dogs and cats are mentioned, no other animals

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.