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timofeeve [1]
1 year ago
13

The construction of copying ∠"QPR" is started below. The next step is to set the width of the compass to the length of ("AB" ).

How does this step ensure that the new angle will be congruent to the original angle?

Mathematics
1 answer:
Roman55 [17]1 year ago
4 0

Answer:

Constant radius, AB = TU

Step-by-step explanation:

Construction: Copying of <QPR, so that;

         <QPR = <TSU

The compass is placed in such a way that its two pointed legs are place at points A and B respectively to copy distance AB.

Now, place the compass at T and describe an arc to locate point U. Draw a straight line through S and U.

Therefore,

             <QPR = <TSU

The step ensures that the angles are congruent by constant radius, AB = TU.

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If quadrilateral PQRS is a rectangle, then which of the following is true?
brilliants [131]

∠STP ≅ ∠QTR is the True statement ⇒ answer C

Step-by-step explanation:

In any rectangle

1. Each two opposite sides are equal and parallel

2. The measure of its vertex angles is 90°

3. The two diagonals are equal

Now lets find the true statements

∵ PQRS is a rectangle

∴ PS = QR ⇒ opposite sides

∴ PQ = SR ⇒ opposite sides

∴ PR = QS ⇒ diagonals

A.  ∠PSQ ≅ ∠QSR

∵ The diagonals of the rectangle do not bisect the vertex angles

∴ AQ does not bisect angle S

∴  m∠PSQ ≠ m∠QSR

∴  ∠PSQ not congruent ∠QSR

∠PSQ ≅ ∠QSR ⇒ False

B. segment SR ≅ segment RQ

∵ SR and RQ are two adjacent sides

∵ The adjacent side in the rectangle not equal

∴ SR ≠ QR

∴ segment SR not congruent to segment RQ

segment SR ≅ segment RQ ⇒ False

C. ∠STP ≅ ∠QTR

∵ PR intersects QS at point T

∴ m∠STP = m∠QTR ⇒ vertically opposite angles

∴ ∠STP ≅ ∠QTR

∠STP ≅ ∠QTR ⇒ True

D. segment PS ≅ segment PR

∵ PS is a side in the rectangle

∵ PR is a diagonal in the rectangle

∵ The side of the rectangle not equal the diagonal of the rectangle

∴ PS ≠ PR

∴ segment PS not congruent to segment PR

segment PS ≅ segment PR ⇒ False

∠STP ≅ ∠QTR is the True statement

Learn more:

You can learn more about rectangle in brainly.com/question/6594923

#LearnwithBrainly

8 0
2 years ago
Read 2 more answers
What is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6
Mashutka [201]
The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.
4 0
2 years ago
F is directly proportional to a.<br>If F = 42 when a 7 find<br>a when F = 18<br>​
horrorfan [7]

Answer:

a=3

Step-by-step explanation:

The formula for direct proportion is

f = ka

Let f= 42 and a = 7

42 = k*7

Divide each side by 7

42/7 = k7/7

6 =k

f = 6a

Let f = 18

18 = 6a

Divide each side by 6

18/6 = 6a/6

3 =a

7 0
2 years ago
Read 2 more answers
A solid cylindrical metal is melted and recast into cubes of metal of sides 3cm . The base radius of the initial cylindrical met
belka [17]

Answer:

808

Step-by-step explanation:

The volume of the initial cylindrical metal must be equal to the total volume of the cubes.

Let the number of cubes made be x. Therefore:

V_C = V_c * x

where V_C = volume of the cylinder

V_c = volume of each cube

Each of the cubes have sides of length 3 cm.

The volume of a cube is given as:

V_c = L^3

where L = length of side of cube

Therefore, the volume of each cube is:

V_c = 3^3 = 27 cm^3

The volume of a cylinder is given as:

V_C = \pi r^2h

where r = radius

h = height of the cylinder

The volume of the cylinder is:

V_C = \pi * 10.5^2 * 63 = 21823.55 cm^3

Therefore:

21823.55 = 27 * x

=> x = 21823.55 / 27

x = 808.27

Since the number of cubes can only be a whole number, the number of cubes that will be made is 808.

8 0
2 years ago
a box holds nine smaller boxes. each of the smaller boxes holds nine plastic containers. each plastic contai.er holds nine bags.
svp [43]
So, basically ..you just multiply
9*9*9*9
6561
4 0
2 years ago
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