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2 years ago

Which rules would result in a triangle A being congruent to or not congruent to B?

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

3 0

Well the only thing that would make these triangles not congruent is dilation, Thus, translation, reflection, and rotations all make the triangles congruent.

The bottom one and third one are not congruent while everything else is.

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Step-by-step explanation:

$- 18 < 9x$

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2 years ago

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3 years ago

Read 2 more answers

I need to find the surface area and volume of all three figures. If you could provide what equations you used to I will be grate

Margarita [4]

Answer:

Part 1) Sphere The surface area is equal to $SA=196\pi\ m^{2}$ and the volume is equal to $V=\frac{1,372}{3}\pi\ m^{3}$

Part 2) Cone The surface area is equal to $SA=(16+4\sqrt{65})\pi\ units^{2}$ and the volume is equal to $V=\frac{112}{3}\pi\ units^{3}$

Part 3) Triangular Prism The surface area is equal to $SA=51.57\ mm^{2}$ and the volume is equal to $V=17.388\ mm^{3}$

Step-by-step explanation:

Part 1) The figure is a sphere

a) Find the surface area

The surface area of the sphere is equal to

$SA=4\pi r^{2}$

we have

$r=14/2=7\ m$ ----> the radius is half the diameter

substitute

$SA=4\pi (7)^{2}$

$SA=196\pi\ m^{2}$

b) Find the volume

The volume of the sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=14/2=7\ m$ ----> the radius is half the diameter

substitute

$V=\frac{4}{3}\pi (7)^{3}$

$V=\frac{1,372}{3}\pi\ m^{3}$

Part 2) The figure is a cone

a) Find the surface area

The surface area of a cone is equal to

$SA=\pi r^{2} +\pi rl$

we have

$r=4\ units$

$h=7\ units$

Applying Pythagoras Theorem find the value of l (slant height)

$l^{2}=r^{2} +h^{2}$

substitute the values

$l^{2}=4^{2} +7^{2}$

$l^{2}=65$

$l=\sqrt{65}\ units$

$SA=\pi (4)^{2} +\pi (4)(\sqrt{65})$

$SA=16\pi +4\sqrt{65}\pi$

$SA=(16+4\sqrt{65})\pi\ units^{2}$

b) Find the volume

The volume of a cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

we have

$r=4\ units$

$h=7\ units$

substitute

$V=\frac{1}{3}\pi (4)^{2}(7)$

$V=\frac{112}{3}\pi\ units^{3}$

Part 3) The figure is a triangular prism

a) The surface area of the triangular prism is equal to

$SA=2B+PL$

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the prism

Find the area of the base B

$B=\frac{1}{2} (2.7)(2.3)=3.105\ mm^{2}$

Find the perimeter of the base P

$P=2.7*3=8.1\ mm$

we have

$L=5.6\ mm$

substitute the values

$SA=2(3.105)+(8.1)(5.6)=51.57\ mm^{2}$

b) Find the volume

The volume of the triangular prism is equal to

$V=BL$

where

B is the area of the triangular base

L is the length of the prism

we have

$B=3.105\ mm^{2}$

$L=5.6\ mm$

substitute

$V=(3.105)(5.6)=17.388\ mm^{3}$

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2 years ago