Given parallel lines, which pair of angles are congruent?

Mathematics

1 answer:

Talja [164]2 years ago

4 0

transversal angles

Step-by-step explanation:

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . When the lines are parallel, the corresponding angles are congruent .

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Solve(x+y)^2=(x^2-2xy+y^2) and show your work

Shtirlitz [24]

(x + y)^2 = (x^2 - 2xy + y^2)

First distribute the ^2 on the left side of the equation to each term inside the parenthesis:

x^2+ 2xy + y^2

Now pick one of the variables to solve for and isolate it:

(solving for x)

x^2 + 2xy + y^2 = x^2 - 2xy + y^2

x^2+ 2xy = x^2 - 2xy

2xy = -2xy

-x = x

x = 0

When you solve for y in the equation it will turn out to be 0 as well

7 0

3 years ago

Read 2 more answers

Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?

Lubov Fominskaja [6]

Answer:

yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

For the first parabola, the point of intersection is ...

y^2 = 4(-y-1)

y^2 +4y +4 = 0

(y+2)^2 = 0

y = -2 . . . . . . . . one solution only

x = -(-2)-1 = 1

The point of intersection is (1, -2).

For the second parabola, the equation is the same, but with x and y interchanged:

x^2 = 4(-x-1)

(x +2)^2 = 0

x = -2, y = 1 . . . . . one point of intersection only

___

If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

_____

Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.