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Alex_Xolod [135]
3 years ago
11

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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Effectus [21]

Answer:

P = (65 - R) / 60

Step-by-step explanation:

Raul's grandfather is Miguel

Raul's sister is Paula

We are given that Raul’s age is the same as his grandfather’s age minus 60 times the age of his sister. If we write this mathematically, we have that:

R = M - (60*P)

Where R = Raul's age, M = Miguel's age and P = Paula's age

We are then given that Miguel is 65 years old, this means that M = 65

=> R = 65 - 60P

To find Paula's age, we make P the subject of formula, hence:

60P = 65 - R

=> P = (65 - R) / 60

We can use this expression to find Paula's age.

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Answer:

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Step-by-step explanation:

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ANSWER:

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