Task
In the picture given below, line segments AD and BC intersect at X.
Line segments AB and CD are drawn, forming two triangles AXB
and CXD.
D
B
In each part (a)-(d) below, some additional assumptions about the
picture are given. In each problem, determine whether the given
assumptions are enough to prove that the two triangles are similar;
and if so, what the correct correspondence of vertices is. If the two
triangles must be similar, prove this result by describing a
sequence of similarity transformations that maps one triangle to
the other. If not, explain why not.
a. The lengths AX and XD satisfy the equation 2AX = 3XD.
b. The lengths AX, BX, CX, and DX satisfy the equation AX = DX
c. Lines AB and CD are parallel.
d. Angle XAB is congruent to angle XCD.

u rich

step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

step-by-step explanation: 2