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4 years ago

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A pair of parallel lines is cut by a transversal, as shown below: A pair of parallel lines is cut by a transversal. The exterior

angle made on the right by the intersection of the upper parallel line and the transversal is labeled as p. The exterior angle made on the left by the intersection of the lower parallel line and the transversal is labeled as q. Which of the following best represents the relationship between angles p and q? p = 180 degrees − q q = 180 degrees − p p = 2q p = q

2 answers:

Furkat [3]4 years ago

6 0

Answer:

b: Lines p and q are parallel because alternate exterior angles are congruent

Step-by-step explanation:

STatiana [176]4 years ago

3 0

Because they are alternate exterior angles, they are the same.

So the best relationship from the given is: p = q

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4 years ago

Ava wants to draw a parallelogram on the coordinate plane. She

wolverine [178]

Answer:

$k =(2,1)$

$JK = 2$

Step-by-step explanation:

Given

$J = (0,1)$ ---- $(x_1,y_1)$

$H = (1,-2)$ --- $(x_2,y_2)$

$I = (3,-2)$ --- $(x_3,y_3)$

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:

$\frac{1}{2}(I + J) = \frac{1}{2}(H+K)$

$\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)$

$\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)$

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$(3,-1) = (1+x,-2+y)$

By comparison:

$1 + x = 3$

$-2 + y = -1$

Solve for x and y

$x = 3 - 1 =2$

$y = -1 +2 = 1$

So, the coordinates of k is:

$k =(2,1)$

The length of JK is calculated using distance (d) formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

$J = (0,1)$ ---- $(x_1,y_1)$

$k =(2,1)$ ---- $(x_2,y_2)$

So:

$d = \sqrt{(0 - 2)^2 + (1 - 1)^2$

$d = \sqrt{(- 2)^2 + (0)^2$

$d = \sqrt{4 + 0$

$d = \sqrt{4$

$d = 2$

Hence:

$JK = 2$

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3 years ago