Question

plot the coordinates on the plane. then determine whether ab and cd are congruent.

1. a(6, -1), b(1, -1), c(2, -3), d(4, -3)
2. a(3,6), b(3,0), c(-4,5), d(2,5)

find the indicated value.

1. if rt = 36, find the value of x.

(diagram: r---s---t, rs=6x+1, st=x+7)

1. if df = 9x - 39, find the value of ef.

(diagram: d---e---f, de=47, ef=3x+10)

1. if uw = 6x - 35, find uw.

(diagram: u---v---w, uv=19, vw=4x-20)

1. if hj = 7x - 27, find the value of x.

(diagram: h---i---j, hi=3x-5, ij=x-1)

1. if bd = 7x - 10, bc = 4x - 29, and cd = 5x - 9, find each value.

x = ______
bc = ______
cd = ______
bd = ______

Explanation:

Problem 1:

Step1: Find length of AB

Since A(6, -1) and B(1, -1) have the same y - coordinate, the distance \( AB=\vert6 - 1\vert=5\)

Step2: Find length of CD

Since C(2, -3) and D(4, -3) have the same y - coordinate, the distance \( CD=\vert4 - 2\vert = 2\)

Step3: Compare AB and CD

Since \(5
eq2\), AB and CD are not congruent.

Step1: Find length of AB

Since A(3,6) and B(3,0) have the same x - coordinate, the distance \( AB=\vert6 - 0\vert=6\)

Step2: Find length of CD

Since C(-4,5) and D(2,5) have the same y - coordinate, the distance \( CD=\vert2-(-4)\vert=\vert2 + 4\vert=6\)

Step3: Compare AB and CD

Since \(AB = CD=6\), AB and CD are congruent.

Step1: Set up the equation

From the line segment, \(RT=RS + ST\), so \(36=(6x + 1)+(x + 7)\)

Step2: Simplify the equation

\(36=6x + 1+x + 7=7x+8\)

Step3: Solve for x

Subtract 8 from both sides: \(36 - 8=7x\), \(28 = 7x\), divide both sides by 7: \(x = 4\)

Answer:

AB and CD are not congruent.

Problem 2: