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masha68 [24]
2 years ago
12

These are isosceles equatorial triangle questions

Mathematics
1 answer:
vovikov84 [41]2 years ago
6 0

Answer:

Step-by-step explanation:

1) ABCD rectangle

In Δ ABE

∠BAE +  ∠B + ∠AEB = 180 {angle sum property}

   39 + 90 + ∠AEB = 180

             129 + ∠AEB = 180

                       ∠AEB = 180 - 129

                      ∠AEB = 51

∠AEB + ∠AED + ∠CED = 180      {Straight line angles}

            51 + x + 66 = 180

              117 + x  = 180

                      x = 180 - 117

                    x = 63

2) XYZ  equilateral triangle

In equilateral triangle each angle = 60°

∠XZY = 60

∠XZY + ∠XZW = 180            {linear pair}

 60+ ∠XZW = 180

            ∠XZW = 180 - 60

∠XZW = 120

In ΔXZW,

120 + 35 +x = 180  {angle sum property of triangle}

        155 +x = 180

                 x = 180 - 155

                x = 25

PQR isosceles triangle

PQ = PR

∠PRQ = ∠Q =  69°

∠PRS + ∠PRQ = 180   {linear pair}

 ∠PRS + 69 = 180

        ∠PRS = 180 - 69

        ∠PRS = 111

In ΔPRS

x + 111 + 31 = 180         {Angle sum  property of triangle}

         x + 142 = 180

                x = 180 - 142

              x = 38

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After translation:

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After dilation:

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Step-by-step explanation:

Given the vertices of the Quadrilateral WXYZ

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As the rule of translation is given by

Translation: (x, y)  →  (x-6, y-8)

So, after the translation the vertices of Quadrilateral WXYZ will be translated as:

W(-4, 8)  →  (x-6, y-8) ⇒ (-4-6, 8-8) = W'(-10, 0)

X(-4, 0)  →  (x-6, y-8) ⇒ (-4-6, 0-8) = X'(-10, -8)

Y(-12, 4)  →  (x-6, y-8) ⇒ (-12-6, 4-8) = Y'(-18, -4)

Z(-8, 16)  →  (x-6, y-8) ⇒ (-8-6, 16-8) = Z'(-14, 8)

Therefore,

W'X'Y'Z' = W'(-10, 0), X'(-10, -8), Y'(-18, -4), Z'(-14, 8)

Next, the rule of dilation is given by

Dilation: (x, y)  →  (2x, 2y), centered at (0, 0)

W'(-10, 0)  →  (2x, 2y) ⇒ (2(-10), 2(0)) = W'' (-20, 0)  

X'(-4, 0)  →  (2x, 2y) ⇒ (2(-4), 2(0)) = X'' (-8, 0)

Y'(-12, 4)  →  (2x, 2y) ⇒ (2(-12), 2(4)) = Y'' (-24, 8)

Z'(-8, 16)  →  (2x, 2y) ⇒ (2(-8), 2(16)) = Z'' (-16, 32)

Therefore,

W''X''Y''Z'' = W'' (-20, 0), X'' (-8, 0) , Y'' (-24, 8), Z'' (-16, 32)

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