Thomas needs to prove the following theorem: If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram.
He draws the figure below and begins his proof.

Prove: ABCD is a parallelogram

What should be Thomas's reason for Step 2?

If parallel lines are cut by a transversal, corresponding angles are congruent.

A) Vertical angles are congruent.
B) If parallel lines are cut by a transversal, alternate interior angles are congruent.
C) Congruent parts of congruent triangles are congruent
D) If parallel line are cut by a transversal, corresponding angles are congruent

Answer is in the photo. I couldn't attach it here, but uploaded it to a file hosting. link below! Good Luck!

cutt.ly/XzW3SUN

D

Step-by-step explanation:

It's parrallel. so it's the answer.

d) 48

step-by-step explanation:

16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336

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.