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Law Incorporation [45]
3 years ago
6

HELP! WILL GIVE BRAINLIEST! DO NOT TAKE ANSWERS OFF ONLINE, THEY ARE WRONG!!!! The following is an incomplete paragraph proving

that the opposite sides of parallelogram ABCD are congruent: Parallelogram ABCD is shown where segment AB is parallel to segment DC and segment BC is parallel to segment AD. According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct a diagonal from A to C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. ________________. Angles BCA and DAC are congruent by the Alternate Interior Angles Theorem. Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent. Which sentence accurately completes the proof? A) Angles ABC and CDA are corresponding parts of congruent triangles, which are congruent (CPCTC). B) Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent). C) Angles BAC and DCA are congruent by the Same-Side Interior Angles Theorem. D) Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem.

Mathematics
1 answer:
ohaa [14]3 years ago
4 0

Answer:

The correct option is B.

Step-by-step explanation:

Given information: AB\parallel DCAB∥DC and BC\parallel ADBC∥AD .

Draw a diagonal AC.

In triangle BCA and DAC,

AC\cong ACAC≅AC (Reflexive Property of Equality)

\angle BAC\cong \angle DCA∠BAC≅∠DCA ( Alternate Interior Angles Theorem)

\angle BCA\cong \angle DAC∠BCA≅∠DAC ( Alternate Interior Angles Theorem)

The ASA (Angle-Side-Angle) postulate states that two triangles are congruent if two corresponding angles and the included side of are congruent.

By ASA postulate,

\triangle BCA\cong \triangle DAC△BCA≅△DAC

Therefore option B is correct

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Water flows at a rate of 9000 cubic inches per minute into a cylindrical tank. the tank has a diameter of 144 inches and a heigh
valkas [14]
V = π*r^2*h
(9000 in^3/min)*(10 min) = π*(72 in)^2*h
h = (90,000 in^3)/(5184π in^2) ≈ 5.5 in
8 0
4 years ago
Read 2 more answers
Find the area of the shape shown below.
valkas [14]

Answer:

<h2><em><u>12 is the total area</u></em></h2>

Step-by-step explanation:

A of triangle = 1/2 * b * h

b = 6

h = 2

2 * 6 * 0.5

= 12 * 0.5

<h2><em><u>= 6</u></em></h2>

A of square = l * w

2 * 2

<h2><em><u>= 4</u></em></h2>

A of Triangle = 1/2 * b * h

2 * 2 * 0.5 =

4 * 0.5

<h2><em><u>= 2</u></em></h2>

2 + 4 + 6

= 6 + 6

<h2><em><u>= 12</u></em></h2>
6 0
3 years ago
Help please inequalities are kicking my butt any help is greatly appreciated thank you in advance
Hitman42 [59]

Answer:

Correct option is (C)

Step-by-step explanation:

we are given that -Tim design a pair of shorts,S, and T-shirts,t.

Tim sell Sorts for $12 and T-shirts for $8 each.

Tim can work atmost 18 hours a day so we can write time\leq 18

Time taken to design a T-shirt is 30 minutes and for Shorts, it is 45 minutes.

\frac{30}{60}t+\frac{45}{60}s\leq   18\\\text{Multiply both the sides by 60}\\30t+45s\leq 1080\\\text{Divide both the sides by 45}\\s+0.66t\leq 24\\\text{Subtract 0.66t from both the sides}\\s\leq 24-0.66t

He must design 12 itesm each day, so we can write t+s\geq 12

Further it can be written as

t+s\geq 12\\\text{Subtract t from both the sides}\\s\geq 12-t

Also Tim can not design more than 30 items in one day, so we can write

t+s\leq 30\\\text{Subtsract t from both the sides}\\s\leq 30-t

Hence from the above equations , its claer that

s\geq 12-t,s\leq 30-t,s\leq 24-0.66t,s\geq 0,t\geq 0

7 0
4 years ago
I need help please. How do I find the value of x?
Zina [86]
X = 58

The angle directly across from the 32 is also 32 degrees because it uses the same lines at the same angles. That's the Vertical Angles Theorem. The line straight across means that is 180 degrees, which is already split in half by the visible 90 degree angle (given by the box in the corner). Since all the angles are on the same side of the line, the 180 degree angle, they should add up to equal 180 degrees. Also, since 90 is half of 180, the 32 degree angle and the x angle should just add up to equal 90 degrees. So, 90 minus 32 equals 58.
7 0
3 years ago
Which trig ratio<br> determine which trig ratio to use to solve for x
maw [93]

Answer:

sin = opp / hyp

cos = Adj / hyp

tan = opp / adj


7. cos 41 = x / 86

8. sin x = 5/13

9. cos x = 9/37

10. tan 61 = x/28

11. sin 41 = x/65

12. tan x = 79/84

Step-by-step explanation:

5 0
2 years ago
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