Triangle abc is isosceles. what is the length of ? 11 23 40 60

An isosceles triangle is a triangle that has two of its sides equal and also two equal angles.

The length of line BC is 40

So,

line AB = x + 17

line BC = 2x - 6

equate the line

line AB = line BC

x + 17 = 2x - 6

x - 2x = -6 - 17

- x = - 23

x = 23

substitute x = 23 into

line AB = x + 17

= 23 + 17

= 40

line BC = 2x - 6

= 2(23) - 6

= 46 - 6

= 40

Therefore, the length of line BC is 40

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An isosceles triangle is a triangle that has 2 congruent/equal sides and 2 congruent angles.

Side AB and side BC are the same length (the red tick marks shows that the sides are congruent)

Since they are the same length, you can set them equal to each other

Side AB = Side BC

x + 17 = 2x - 6        Subtract x on both sides

17 = x - 6       Add 6 on both sides

23 = x

Now that you know "x", you can find the length of Side BC:

2x - 6      Plug in 23 for "x"

2(23) - 6

46 - 6 = 40

The length of BC is 40

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

yes

step-by-step explanation:

they have to be opposite and reciprocal of eachother.