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gayaneshka [121]
3 years ago
6

Find the surface area of the prism.

Mathematics
1 answer:
KonstantinChe [14]3 years ago
6 0
C. 94 m^2 is the surface area
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If you are using this figure to prove the isosceles triangle theorem which of the following would be the best strategy
Tpy6a [65]

If two sides of a triangle are <span>congruent </span>, then the angles opposite to these sides are congruent.

 

<span><span>∠P≅∠Q</span><span>∠P≅∠Q</span></span>

Proof:

Let <span>SS</span> be the midpoint of <span><span><span>PQ</span><span>¯¯¯¯¯</span></span><span><span>PQ</span>¯</span></span> .

Join <span>RR</span> and <span>SS</span> .

Since <span>SS</span> is the midpoint of  <span><span><span>PQ</span><span>¯¯¯¯¯</span></span><span><span>PQ</span>¯</span></span> , <span><span><span><span>PS</span><span>¯¯¯¯¯</span></span>≅<span><span>QS</span><span>¯¯¯¯¯</span></span></span><span><span><span>PS</span>¯</span>≅<span><span>QS</span>¯</span></span></span> .

By <span>Reflexive Property </span>,

<span><span><span><span>RS</span><span>¯¯¯¯¯</span></span>≅<span><span>RS</span><span>¯¯¯¯¯</span></span></span><span><span><span>RS</span>¯</span>≅<span><span>RS</span>¯</span></span></span>

It is given that <span><span><span><span>PR</span><span>¯¯¯¯¯</span></span>≅<span><span>RQ</span><span>¯¯¯¯¯</span></span></span><span><span><span>PR</span>¯</span>≅<span><span>RQ</span>¯</span></span></span>

Therefore, by <span>SSS </span>,

<span><span>ΔPRS≅ΔQRS</span><span>ΔPRS≅ΔQRS</span></span>

Since corresponding parts of congruent triangles are congruent,

<span><span>∠P≅∠Q</span><span>∠P≅∠Q</span></span>

The converse of the Isosceles Triangle Theorem is also true.

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

If <span><span>∠A≅∠B</span><span>∠A≅∠B</span></span> , then <span><span><span><span>AC</span><span>¯¯¯¯¯</span></span>≅<span><span>BC</span><span>¯¯¯¯¯</span></span></span><span><span><span>AC</span>¯</span>≅<span><span>BC</span>¯</span></span></span> .

 

7 0
3 years ago
(Photo) Which table shows a relation that is not a function?
san4es73 [151]
Uhm prob d. I’m not very sure though but I’m pretty sure
5 0
3 years ago
Which of the following is the estimated sum of fifty-five, sixty, and sixty-five using compatible numbers?
SVEN [57.7K]

C. 190

Round each number

55→60.

60→60

65→70

Then add all of your rounded numbers.

60+60+70=190

3 0
3 years ago
HELPPPPPPPPP best answer will get braainliest
ValentinkaMS [17]
180 (and then whatever the units of measure are)

to find the perimeter you have to add all four sides together to get your total. (3y+2)+(3y+2)+(5y+8)+(5y+8)

y=180
4 0
2 years ago
Read 2 more answers
Triangle ABC has vertices at A(-4, -2), B(1, 7) and C(8, -2)
Arada [10]

Answer:

a). Area = 54 square units

b). Perimeter = 33.7 units

Step-by-step explanation:

Vertices of the triangle ABC are A(-4, -2), B(1, 7) and C(8, -2).

(a). Area of the triangle ABC = \frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})] (Absolute value)

By substituting the values from the given vertices,

Area = \frac{1}{2}[(-4)(7+2)+(1)(-2+2)+8(-2-7)]

        = \frac{1}{2}[-36+0-72]

        = \frac{1}{2}(-108)

        = (-54) unit²

Therefore, absolute value of the area = 54 square units

(b). Distance between two vertices (a, b) and (c, d)

        d = \sqrt{(a-c)^{2}+(b-d)^2}

     AB = \sqrt{(-4-1)^{2}+(-2-7)^{2}}

           = \sqrt{106}

           = 10.295 units

     BC = \sqrt{(1-8)^2+(7+2)^2}

           = \sqrt{130}

           = 11.402 units

     AC = \sqrt{(-4-8)^2+(-2+2)^2}

           = 12 units

     Perimeter of the triangle = AB + BC + AC = 10.295 + 11.402 + 12

                                                                          = 33.697

                                                                          ≈ 33.7 units

7 0
3 years ago
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