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makkiz [27]
3 years ago
12

10. Provide the reasons for the following proof:

Mathematics
2 answers:
lana [24]3 years ago
6 0

Answer:

The reason for third statement is reflexive property and the reason for fourth statement is SAS.

Step-by-step explanation:

Given information: WX\cong XY and XZ bisects angle WXY.

To prove: \trinagle WXZ\cong \triangle YXZ

Statement                                                        Reason

WX\cong XY                                     (Given)

\angle WXZ\cong \angle YXC         (XZ bisects angle WXY)

XZ\cong ZX                                      (Reflexive property)

\trinagle WXZ\cong \triangle YXZ   SAS

Reflexive property states that a line is congruent to itself.

SAS postulate states that two triangle are congruent If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle.

Therefore the reason for third statement is reflexive property and the reason for fourth statement is SAS.

inessss [21]3 years ago
3 0
Given that <span>Line WX is congruent to Line XY and Line XZ bisects Angle WXY.

We prove that triangle WXZ is congruent to triangle YXZ as follows:

\begin{tabular}&#10;{|c|c|}&#10;Statement&Reason\\[1ex]&#10;\overline{WX}\cong\overline{XY},\ \overline{XZ}\ bisects\ \angle WXY&Given\\&#10;\angle WXY\cong\angle YXZ & Deifinition of an angle bisector\\&#10;\overline{XZ}\cong\overline{ZX}&Refrexive Property of \cong\\&#10;\triangle WXZ\cong\triangle YXZ&SAS&#10;\end{tabular}</span>
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Pentagon ABCDE and pentagon A″B″C″D″E″ are shown on the coordinate plane below:
erastova [34]

The transformations that are applied to pentagon ABCDE to create A"B"C"D"E" are:

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2) Reflection across the x-axis (x, y) → (x, -y)

So, the overall transformation given in the graph is (x, y) → {(x + 8), -(y + 2)}.

<h3>What are the transformation rules?</h3>

The transformation rules are:

  • Reflection across x-axis: (x, y) → (x, -y)
  • Reflection across y-axis: (x, y) → (-x, y)
  • Translation: (x, y) → (x + a, y + b)
  • Dilation: (x, y) → (kx, ky)

<h3>Calculation:</h3>

The pentagons in the graph have vertices as

For the pentagon ABCDE: A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), and (-2, 4)

For the pentagon A"B"C"D"E": A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), and E"(6, -6)

Consider the vertices A(-4, 5) from the pentagon ABCDE and A"(4, -7) from the pentagon A"B"C"D"E".

Applying the Translation rule for the pentagon ABCDE:

The rule is (x, y) → (x + a, y + b)

So, the variation is

-4 + a = 4

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5 + b = 7

⇒ b = 7 - 5 = 2

So, the pentagon ABCDE is translated by (x + 8, y + 2).

Applying the Reflection rule for the translated pentagon:

The translated pentagon has vertices (x + 8, y + 2).

When applying the reflection across the x-axis,

(x + 8, y + 2) → {(x + 8), -(y + 2)}

Therefore, the complete transformation of the pentagon ABCDE to the pentagon A"B"C"D"E" is (x, y) → {(x + 8), -(y + 2)}

Verification:

A(-4, 5) → ((-4 + 8), -(5 + 2)) = (4, -7)A"

B(-6, 4) → ((-6 + 8), -(4 + 2)) = (2, -6)B"

C(-5, 1) → ((-5 + 8), -(1 + 2)) = (3, -3)C"

D(-2, 2) → ((-2 + 8), -(2 + 2)) = (6, -4)D"

E(-2, 4) → ((-2 + 8), -(4 + 2)) = (6, -6)E"

Learn more about transformation rules here:

brainly.com/question/4289712

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