Answered

Are quadrilaterals ABCD and EFGH similar?


Yes, quadrilaterals ABCD and EFGH are similar because a translation of (x + 2 y + 4) and a dilation by the scale factor of 2 from point D' map


quadrilateral ABCD onto EFGH.


Yes, quadrilaterals ABCD and EFGH are similar because a translation of (x + 3. y + 4) and a dilation by the scale factor of 2 from point A' map


quadrilateral ABCD onto EFGH.


No, quadrilaterals ABCD and EFGH are not similar because their corresponding angles are not congruent.


No quadrilaterals ABCD and EFGH are not similar because their corresponding segments are not proportional.

Answer :

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Answer:

No quadrilaterals ABCD and EFGH are not similar because their corresponding segments are not proportional.

Step-by-step explanation:

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For the quadrilaterals to be similar, their corresponding angles will be equal.

The correct option in response to question if the quadrilaterals ABCD and EFGH are equal is; No quadrilateral ABCD and EFGH are not similar because their corresponding segments are not proportional.

Reasons:

The vertex points of quadrilateral ABCD are;

A(0, 0), B(2, 0), C(3, -2), and D(-1, -2)

E(2, 4), F(6, 4), G(7, 1), and H(1, 1)

In quadrilateral EFGH, we have;

∠EHG = arctan(slope of EH)

Therefore;

  • [tex]\angle EHG = arctan \left(\dfrac{4 - 1}{2 - 1} \right) \approx 71.6 ^{\circ}[/tex]

In quadrilateral ABCD, we have;

∠ADC = arctan(slope of AD)

Therefore;

  • [tex]\angle ADC= arctan \left(\dfrac{0 - (-2)}{0 - (-1)} \right) \approx 63.4^{\circ}[/tex]

Given that ∠EHG and ∠ADC are corresponding angels and are not equal,

we have that the two quadrilaterals are not similar.

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