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3 years ago

Which reason completes the proof below?

Mathematics

1 answer:

sergeinik [125]3 years ago

4 0

Observe the figure given.

Given: ABCD is a parallelogram.

To prove: ABCD is a rhombus

Statement

1. ABCD is a parallelogram. AC bisects $\angle BCD, \angle BAD$ .

Reason: Given

2. $\angle 1 \cong \angle 2, \angle 3 \cong \angle 4$

Reason: Definition of an angle bisector

3. $AC \cong AC$

Reason: Reflexive property of congruence

4. $\Delta ABC \cong \Delta ADC$

Reason: ASA Postulate

5. $AB \cong AD, BC \cong DC$

Reason: corresponding parts of congruent triangles are equal.

6. $AB \cong CD, BC \cong AD$

Reason: Opposite sides of the parallelogram are congruent.

7. $AB \cong AD \cong BC \cong CD$

Reason: Transitive property of congruence

8. ABCD is a rhombus

Reason: Definition of rhombus

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Answer:

The scale factor is

$\frac{1}{3}$

Step-by-step explanation:

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2 years ago

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3 years ago

√-225 • √-36 . show work.

Darya [45]

Answer:

±90

Step-by-step explanation:

√(-225) · √(-36) = (15i)·(6i) = 90i² = 90·(-1) = -90

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On the other hand, ...

... √(-225) · √(-36) = √((-225)·(-36)) = √8100 = 90

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If you consider all the roots at each stage, the result is ±90. Since you're working with complex numbers here, it is reasonable to recognize every number has two square roots.

... √(-225) = ±15i

... √(-36) = ±6i

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