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2 years ago

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Given: ABCD is a quadrilateral, Segment AB is congruent to Segment CD, <1 is congruent to <2 Prove: ABCD is a parallelogra

m

1 answer:

tiny-mole [99]2 years ago

6 0

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.

We need to prove that ABCD is a parallelogram.

<h3>How to prove a given quadrilateral is a parallelogram?</h3>

If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.

From the given quadrilateral ABCD:

AB=CD (Given)

∠1=∠2 (Given)

AC=AC (Diagonal)

From ASA congruency ΔABC and ΔADC are congruent.

By CPCT, AD=BC and ∠ABC=∠ADC.

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

To learn more about parallelogram visit:

brainly.com/question/1563728.

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FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:

luda_lava [24]

The value of the probability P(A) is 0.40

<h3>How to determine the probability?</h3>

The given parameters about the probability are

P(A or B) = 0.6

P(B) = 0.3

P(A and B) = 0.1

To calculate the probability P(A), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

0.1 = 0.3 + P(A) - 0.6

Collect the like terms

P(A)= 0.1 - 0.3 + 0.6

Evaluate the expression

P(A)= 0.4

Hence, the value of the probability P(A) is 0.40

Read more about probability at

brainly.com/question/25870256

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3 0

2 years ago

Pls help is it A. B. C. D.

Ivenika [448]

Answer:

C

Step-by-step explanation:

Hope I was able to help!! :)

7 0

3 years ago

haily brought m pencils for $0.50 each and n pens for 0.75 each. She spent 0.5m+0.75n dollars. what does the term 0.75n represen

SpyIntel [72]

Answer:

It represents n pens bought

6 0

2 years ago

Suppose researchers test 100 college students, whose ages range from 18 to 23. They also test 100 people at a nearby community c

prisoha [69]

Answer:

b. You would conclude that the differences in the average scores can be traced to differences in the working memory of the two groups.

Step-by-step explanation:

Though the average scores of the two sets could have lead to various conditions, but retentive ability deminishes with respect to an increase in age. With respect to the age of the elderly people involved, it is expected that some of them would not be able to retain information for a long period of time. Thus, their average score is 72%.

The college students' are younger, so it is expected that they should be able to retain more information. That ability is one of the reasons why their average score is 85%.

It can be concluded from the research that the differences in the average scores is probably due to the working memory of the two groups.

6 0

3 years ago

If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),

nikklg [1K]

Step-by-step explanation:

<u>Step 1: Solve using the first point</u>

<em>(2, 28)</em>

$28 = a(2)^3 + b(2)^2 + c(2) + d$

$28 = 8a + 4b + 2c + d$

<u>Step 2: Solve using the second point</u>

<em>(-1, -5)</em>

$-5 = a(-1)^3 + b(-1)^2 + c(-1) + d$

$-5 = -a + b - c + d$

<u>Step 3: Solve using the third point</u>

<em>(4, 220)</em>

$220 = a(4)^3 + b(4)^2 + c(4) + d$

$220 = 64a + 16b + 4c + d$

<u>Step 4: Solve using the fourth point</u>

<em>(-2, -20)</em>

$-20 = a(-2)^3 + b(-2)^2 + c(-2) + d$

$-20 = -8a + 4b - 2c + d$

<u>Step 5: Combine the first and fourth equations</u>

<u /> $28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d$

$8 = 8b + 2d$

$8 - 8b = 8b - 8b + 2d$

$(8 -8b)/2 = 2d/2$

$4 - 4b = d$

<u>Step 6: Solve for c in the second equation</u>

$-5 + 5 = -a + b - c + d + 5$

$0 + c = -a + b - c + c + d + 5$

$c = -a + b + d + 5$

<u>Step 7: Substitute d with the stuff we got in step 5</u>

$c = -a + b + (4 - 4b) + 5$

$c = -a + b + 4 - 4b + 5$

$c = -a - 3b + 9$

<u>Step 8: Substitute d and c into the first equation</u>

<u /> $28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)$

$28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b$

$28 - 22 = 6a - 6b + 22 - 22$

$6 / 6 = (6a - 6b) / 6$

$1 + b = a - b + b$

$1 + b = a$

<u>Step 9: Substitute a, b, and c into the third equation</u>

$220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)$

$220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b$

$220 - 100 = 60b + 100 - 100$

$120 / 60 = 60b / 60$

$2 = b$

<u>Step 10: Find a using b = 2</u>

$a = b + 1$

$a = (2) + 1$

$a = 3$

<u>Step 11: Find c using a = 3 and b = 2</u>

$c = -a - 3b + 9$

$c = -(3) - 3(2) + 9$

$c = -3 - 6 + 9$

$c = 0$

<u>Step 12: Find d using b = 2</u>

$d = 4 - 4b$

$d = 4 - 4(2)$

$d = 4 - 8$

$d = -4$

Answer: $a = 3, b = 2, c = 0,d = -4$

6 0

3 years ago

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