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3 years ago

Which Triangles are congruent by ASA

Mathematics

2 answers:

PolarNik [594]3 years ago

8 0

Triangles congruent by ASA have two pairs of congruent sides and an included congruent angle.

The graph indicates that sides TV, HG, and AB are congruent, and that sides TU, FG, and BC are congruent. It also indicates that angles U, F, and C are congruent, and that angles G and B are congruent. Notice that angle U of triangle TUV is not an included angle; this eliminates triangle TUV as it can't be congruent to another triangle by ASA with the information provided.

That leaves triangles FGH and ABC. Evidently, angles G and B are included angles, so these triangles are congruent by ASA.

Answer:
b. ΔHGF and ΔABC

sweet-ann [11.9K]3 years ago

6 0

Answer:

b. $\triangle HGF\cong \triangle ABC$

Step-by-step explanation:

We are given that three triangles VTU,HGF and ABC.

We have to find the triangle which are congruent by ASA.

ASA postulate: When two angles of one triangle and side on which two equal angles are made are congruent to its corresponding two angles and corresponding side of other triangle then, two triangles are congruent by ASA.

From given figure, we can see that

AB=HG=VT

BC=FG=TU

$\angle V=\angle F=\angle C$

$\angle G=\angle B$

Therefore, $\triangle HGF\cong \triangle ABC$

By ASA postulate because two angle of triangle HGF angle F and angle G and one side FG are congruent to corresponding angles C and B and corresponding side BC.

Option b is true.

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Show 326 using hundreds, tens, and ones

Amiraneli [1.4K]

Answer:

using hunreds 300

using tens 20

using ones 6

300+20+6= 326

Step-by-step explanation:

All you got to do is break them apart into the places.

Plzzz mark brainlest and thank me

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4 years ago

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

3 years ago

A building in a city has a rectangular base. the length of the base measures 65 ft less than twice the width. the perimeter of t

dybincka [34]

By solving a system of equations, we will see that the width is 170ft and the length 275 ft.

<h3>How to get the dimensions of the base?</h3>

For a rectangle of length x and width y, the perimeter is:

P = 2*(x + y).

Here we know that:

x = 2y - 65ft

p = 890ft = 2(x + y)

So we have a system of equations.

To solve this, we need to replace the first equation into the second one:

890ft = 2(x + y)

890ft = 2(( 2y - 65ft) + y)

Now we can solve this for y.

890ft = 4y - 130ft + 2y

890ft + 130ft = 6y

1020ft/6 = y = 170ft

So the width is 170ft, and we know that:

x = 2y - 65ft = 2*(170ft) - 65ft = 275ft

So the length is 275 ft.

If you want to learn more about systems of equations:

brainly.com/question/13729904

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2 years ago

The sum of three times the larger of two integers and twice the smaller is seven the difference between the two integers is four

Aloiza [94]

Answer:

x=3 y=-1

Step-by-step explanation:

3x+2y=7

x-y=4

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3 years ago

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igor_vitrenko [27]

Answer:

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Step-by-step explanation:

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