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1 year ago

Geometry: Write the theorem or postulate for each of the following, ASAP!!!

Mathematics

1 answer:

beks73 [17]1 year ago

7 0

The theorems or postulates for the given pair of angles are as follows:

2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;

3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;

4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;

5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;

6. ∠4 ≅ ∠8 → Corresponding angles are congruent;

<h3>What are the types of pairs of angles?</h3>

Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.

So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.

Based on their position, they are paired into different categories. Such as:

Interior angles: ∠3, ∠4, ∠5, ∠6

Exterior angles: ∠1, ∠2, ∠7, ∠8

'Alternate interior angles' are the pair of interior angles on the opposite side of the transversal 't'. I.e., (∠3, ∠5), (∠4, ∠6) are congruent.
'Alternate exterior angles' are the pair of exterior angles which are on the opposite side of the transversal 't'. I.e., (∠2, ∠8), (∠1, ∠7) are congruent.
'Consecutive interior angles' are the pair of interior angles which are on the same side of the transversal 't'. I.e., (∠3, ∠6), (∠4, ∠5). These are also called "Supplementary angles" which mean they add up to 180°.
'Consecutive exterior angles' are the pair of exterior angles on the same side of the transversal 't'. I.e., (∠2, ∠7), (∠1, ∠8). These are also called "Supplementary angles" which mean they add up to 180°.
'Vertically opposite angles' are the pair of angles that are opposite to each other at the point of intersection. I.e., (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)
'Corresponding angles' are the pair of consecutive angles in which one of the angles is exterior and the other is interior. I.e., (∠1, ∠5), (∠2, ∠6), (∠4, ∠8), (∠3, ∠7)

<h3>Theorems or postulates for the given pair of angles:</h3>

Classifying the given pair of angles and their corresponding theorems:

2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.

Theorem - "The alternate exterior angles are congruent"

3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.

Theorem - "The verticle angles are congruent"

4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.

Theorem - "The alternate interior angles are congruent"

5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.

Theorem - " The supplementary angles add up to 180°"

6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.

Theorem - " The corresponding angles are congruent".

Learn more about the pair of angles here:

brainly.com/question/18772057

#SPJ1

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Which ordered pair comes from the table

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Answer:

B: (6, 5)

Step-by-step explanation:

If you compare the table with the answers, answer B is the only answer that has a matching pair on the table.

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3 years ago

Read 2 more answers

Can someone explain this

horsena [70]

9514 1404 393

Answer:

resultant force: 93.946∠-10.62° N
line of action: 17.314x +92.337y = 809.433

Step-by-step explanation:

We can use the notation a∠b to represent the (x, y) components (a·cos(b), a·sin(b)), where angle b is measured CCW from the +x direction. If we label the forces a, b, c, d clockwise from A, then we have ...

a = 80∠0° = (80, 0)

b = 60∠90° = (0, 60)

c = 90∠45° = (63.640, 63.640)

d = 150∠-110° = (-51.303, -140.954)

If we label point A the origin, then the clockwise torque on point A is the sum of products of the force x-component and its y location, and its y-component and the negative of its x location.

T = (0, 0)·(80, 0) +(3, 0)·(0, 60) +(3, -8)·(63.640, 63.640) +(0, -8)·(-51.303, -140.954)

T = 809.433 . . . . n·m, the CW torque on point A

The sum of forces is ...

F = a +b +c +d = (92.337, -17.314) = 93.946∠-10.62° . . . N

This force, applied to the point of application, must generate the same torque as the given forces. That is ...

F·(y, -x) = 809.433

Then the equation of the line of action is ...

17.314x +92.337y = 809.433 . . . . . x and y in meters measured from A

Any point (x, y) on this line will serve as a point of application of the force. Unfortunately, this line of action does not pass through the rectangular plate. The attachment shows the point (D) on the line of action that is closest to point A.

_____

<em>Additional comment</em>

The resultant force could be decomposed into two forces acting <em>on the rectangular plate</em>. One could be of much larger magnitude, operating at the corner opposite point A. This force would provide the necessary torque. Another would be acting on point A, providing no torque, but with components such that the resultant has the correct magnitude and direction.

6 0

3 years ago

Please help! A-level maths.

astra-53 [7]

$x+y=k\implies y=k-x$

Substitute this into the parabolic equation,

$k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0$

We're told the line $x+y=k$ intersects $C$ twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know

$(-7)^2-4(k+3)=49-4(k+3)>0\implies k$

We can tell from the quadratic equation that $C$ has its vertex at the point (3, 6). Also, note that

$-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5$

and

$-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6$

so the furthest to the right that $C$ extends is the point (5, 2). The line $x+y=k$ passes through this point for $2+5=k\implies k=7$ . For any value of $k$ , the line $x+y=k$ passes through $C$ either only once, or not at all.