Mathematics High School

Unit 6 homework 3 proving triangles similar
Gina Wilon All Things Algebra). 2014

Any help at all would be useful

Unit 6 Homework 3 Proving Triangles Similar Gina Wilon All Things Algebra). 2014Any Help At All Would

Answers

Answer 1

Using the triangle similarity theorems, the given pairs of triangles can be proven to be similar:

1.  [tex]\triangle STR $ and $ \triangle PQN[/tex] are similar by the SSS similarity theorem

2.  [tex]\triangle EFG $ and $ \triangle JHG[/tex] are similar by the AA similarity theorem.

3.  [tex]\triangle XYZ $ and $ \triangle XWT[/tex] are similar by SAS similarity theorem.

4. [tex]\triangle ANF $ and $ \triangle SEH[/tex] are similar by the AA similarity theorem.

5. [tex]\triangle RNQ $ and $ \triangle MNL[/tex] are similar by the SAS similarity theorem.

6. [tex]\triangle ECD $ and $ \triangle LMN[/tex] are similar by the SSS similarity theorem.

7.  [tex]\triangle AEB $ and $ \triangle BDC[/tex] are not similar.

8.  [tex]\triangle JLN $ and $ \triangle KLM[/tex] are similar by the SAS similarity theorem.

9.  [tex]\triangle SUT $ and $ \triangle WUV[/tex] are similar by the AA similarity theorem.

10.  [tex]\triangle DHK $ and $ \triangle BAE[/tex] are similar by the SAS similarity theorem.

The following are triangle similarity theorems that can be used to prove that two triangles are similar if we don't have all the information about the two triangles:

Angle-Angle Similarity Theorem (AA~): two triangles having two congruent triangles that corresponds to each other are similar.

Side-Side-Side Similarity Theorem (SSS~): Two triangles having all three corresponding congruent sides proportional are similar.

Side-Angle-Side Similarity Theorem (SAS~): Two triangles having two corresponding congruent angles and a corresponding included congruent angle in both triangles are similar.

Using the above stated similarity theorems, let's prove the given pairs of triangles are similar or not:

1. [tex]\frac{ST}{PQ} = \frac{SR}{NP} = \frac{TR}{NQ}[/tex]

Plug in the values

[tex]\frac{55}{25} = \frac{44}{20} = \frac{37.4}{17} = 2.2[/tex] (All three sides of one triangle are proportional to all three sides of the other triangle).

Therefore,  [tex]\triangle STR $ and $ \triangle PQN[/tex] are similar by the SSS similarity theorem.

2. <F in [tex]\triangle EFG[/tex] is congruent to <H in [tex]\triangle JHG[/tex]

<EGF in  [tex]\triangle EFG[/tex] is congruent to <JGH in  [tex]\triangle JHG[/tex]

Therefore, [tex]\triangle EFG $ and $ \triangle JHG[/tex] are similar by the AA similarity theorem.

3.<YXZ in [tex]\triangle XYZ[/tex] is congruent to <WXT in [tex]\triangle XWT[/tex]

[tex]\frac{XY}{XW} = \frac{XZ}{XT}[/tex]

Substitute

[tex]\frac{35}{28} = \frac{38}{30} = 1.3[/tex]

This implies that the two corresponding sides of [tex]\triangle XYZ $ and $ \triangle XWT[/tex] are proportional to each other. Also the included angles are congruent.

Therefore, [tex]\triangle XYZ $ and $ \triangle XWT[/tex] are similar by SAS similarity theorem.

4. <A = <S = 29 degrees

<N = <E = 106 degrees (Note: <E = 180 - 29 - 45)

Therefore, [tex]\triangle ANF $ and $ \triangle SEH[/tex] are similar by the AA similarity theorem.

5. <RNQ in [tex]\triangle RNQ[/tex] is congruent to <MNL in [tex]\triangle MNL[/tex] (an included angle is congruent to each other)

[tex]\frac{MN}{NR} = \frac{LN}{NQ} = 1.25[/tex] (two sides of both triangles are proportional)

Therefore, [tex]\triangle RNQ $ and $ \triangle MNL[/tex] are similar by the SAS similarity theorem.

6. [tex]\frac{EC}{LM} = \frac{ED}{LN} = \frac{CD}{MN} = 1.8[/tex]  (three sides of both triangles are proportional).

Therefore, [tex]\triangle ECD $ and $ \triangle LMN[/tex] are similar by the SSS similarity theorem.

7. The information given is not enough to prove that the two triangles are similar by any of the similarity theorems.

Therefore, [tex]\triangle AEB $ and $ \triangle BDC[/tex] are not similar.

8. <JLN in [tex]\triangle JLN[/tex] is congruent to <KLM in [tex]\triangle KLM[/tex] (an included angle is congruent to each other)

[tex]\frac{JL}{KL} = \frac{NL}{ML} = 1.4[/tex] (two sides of both triangles are proportional)

Therefore, [tex]\triangle JLN $ and $ \triangle KLM[/tex] are similar by the SAS similarity theorem.

9. <T = <V = 72 degrees

<SUT = <WUV (Vertical angles)

Therefore, [tex]\triangle SUT $ and $ \triangle WUV[/tex] are similar by the AA similarity theorem.

10. <H = <A = 38 degrees (included angles)

[tex]\frac{AB}{HK} = \frac{AE}{HD} = 1.4[/tex]  (two sides of both triangles are proportional)

Therefore, [tex]\triangle DHK $ and $ \triangle BAE[/tex] are similar by the SAS similarity theorem.

In summary, using the triangle similarity theorems, the given pairs of triangles can be proven to be similar:

1.  similar by the SSS similarity theorem

2.  similar by the AA similarity theorem.

3. similar by SAS similarity theorem.

4. similar by the AA similarity theorem.

5. similar by the SAS similarity theorem.

6. similar by the SSS similarity theorem.

7.  not similar.

8. similar by the SAS similarity theorem.

9. similar by the AA similarity theorem.

10.  similar by the SAS similarity theorem.

Learn more here:

https://brainly.com/question/8762796

Related Questions

Whoever gets this correct gets brain, 5 stars and a thanks! An explanation of it would be amazing! Tysm!

Answers

Answer:

Greatest to Least:

76

8

-53

-274

76 is the highest positive number, which is then followed by 8

The bigger the NEGATIVE number, the least it is. So, -274 is smaller than -53

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Answers

Answer:

Just move 4 spaces up

Step-by-step explanation:

Answer:

left 0 up 4

Step-by-step explanation:

Area of a triangle (can you please show your steps!)

Answers

Answer:

36

Step-by-step explanation:

A=hbb

2=8·9

2=36

Answer:

A= 36

Step-by-step explanation:

A=36

Base= 8

Height= 9

Solution

A=hbb

2=9·8

2=36

I hope this helps

Can someone explain how to do this?

Answers

9514 1404 393

Answer:

  9 and 10

Step-by-step explanation:

Make use of your knowledge of multiplication tables.

  9² = 81

  (√89)² = 89

  10² = 100

√89 lies between 9 and 10

can someone help please?

Answers

Answer:

This is a tricky problem, don't feel bad for not knowing this  :/  I think this is too much in one question even :P  I'll give you the answers and how to get them but really it's going to be a lot to understand in one try.  Pay attention :P

Step-by-step explanation:

first graph the given table .. I use Desmos b/c it's handy

we want y = A[tex]x^{2}[/tex] + bx + c

given   1st      2nd

5          -5          2

0         -3           2

-3        -1           2

-4        1           2

-3        3          2

0         5          2

5          7        

12        

A=2nd / 2  = 2/2 = 1

B=?

C= 5

x=1

y=12

y = a[tex]x^{2}[/tex] + bx +c

12=[tex]1^{2}[/tex] + b(1) +5

12=1+ b +5

6=b   :)

y = [tex]x^{2}[/tex] + 6x +5       ( the answer to a) in the question )  

factor it

(x+5)(x+1)   ( answer to b) in the question

vertex form

y = a(x-h)2 + k

where  h = −b/2a

and k = f( h )

h=6/2(1) = 3

k = [tex]3^{2}[/tex] + 6(3) +5

k=32

y =x-3 + 32  ( answer to c)   in question )

let me know if this worked for you  :)  ( I did this fast late at night :/ )

Please help!!!! asap

Answers

answers:
1. up 5
2. left 5

make (4, 10) and (3, 5) eqaution

Answers

Answer:

y=5x-10

Step-by-step explanation:

To find the slope

rise/run

10-5=5

4-3=1

The slope is 5

Y-intercept

y=5x+b

Use any coordinate for y and x and solve

10=5(4) +b

10=20+b

-10=b

-10 id the y-intercept

Help answer key is on the bottom

Answers

Answer: 4 weeks

Step-by-step explanation:

since you can’t work half a week (in this case) we have to round up

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Answers

find the cost of one bar first
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$0.89 x 5 =$4.45

What is the slope-intercept formula for a line with a rise of 3, a run of 1 and a y-Intercept of 5?

Answers

Answer:

y=3x+5

Step-by-step explanation:

y=mx+b

intercept is 5, postive and represents b

Slope is 3 and represents m

Y jvyouggchkytfkytchgjhvl

10e + 3 < 92

Please reply quickly and explain. I'm having trouble understanding.

Answers

Answer:

10E+3 <92

10(e:6) or any number

10(6)=60+3=63 <92

Step-by-step explanation:

Answer:

10e + 3 < 92

Step-by-step explanation:

Any number times ten plus three is less than 92. Like e = 3, which would be 10(3)+3, or 33. Any number that would make the statement true can be used in the place of e.

what are 3 online websites I can take pictures on with, without saving to ur device , it stays on that site and its just for u?

Answers

the only one i can think of at the moment in pinterest

Step-by-step explanation:

sorry thats all i can think of

Equivalent expression standard form of (2x+5)(x+1)

Answers

i got u mate it’s 2x^2+7x+5 also i recommend getting photo math it’s an app that does it all for u it’s free and it shows the work too !!

Please help me......

Answers

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]A=6*\frac{1}{4} ^2\\\\A=6*\frac{1}{16} \\\\A=\frac{6}{16} \\\\A=\frac{3}{8}[/tex]

Answer:

[tex]A = \frac{3}{8}ft^2[/tex]

Step-by-step explanation:

Using the given formula, [tex]A=6s^2[/tex], and the given value for the side length of the cube, [tex]\frac{1}{4}[/tex] foot, substitute the given value into the equation and solve.

[tex]A=6(\frac{1}{4})^2[/tex]

Remember, setting any value to the second power is the same as multiplying the base (the value that is being squared) by itself. Apply this information to the given problem,

[tex]A = 6(\frac{1}{4}*\frac{1}{4})\\\\A = 6(\frac{1}{16})\\\\A = \frac{6}{16}\\\\A = \frac{3}{8}[/tex]

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Answers

Answer:

52

Step-by-step explanation:

52 is the answer to your question

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Answers

Answer with step-by-step solution:

x^2+8x-9

x^2+9x-x-9

x(x+9)-(x+9)

(x+9)(x-1)

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Answers

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Step-by-step explanation:

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Answers

The right answer is c

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Answers

Answer:

Answer is 46.50

Step-by-step explanation:

I look everywhere and said it was this hehe

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Answers

I think it is 0.3 hope it helps

Answer:

Step-by-step explanation:

Just multiply by 0,3

For EXAMPLE

30% of 100 would be 30

100 x 0,3 = 30

Cory makes a map of his favorite park, using a coordinate system with units of yards. The old oak tree is at position (3, 7) and the granite boulder is at position (-2, 6). How far apart are the old oak tree and the granite boulder? Round to the nearest tenth if necessary

Answers

Answer: 5.09 units

Step-by-step explanation:

Given

Coordinates of Old oak tree are (3,7)

Coordinates of granite boulder are (-2,6)

Distance between them is given by distance formula i.e.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between them is

[tex]\Rightarrow d=\sqrt{(-2-3)^2+(6-7)^2}\\\Rightarrow d=\sqrt{(-5)^2+(-1)^2}\\\Rightarrow d=\sqrt{25+1}=\sqrt{26}\approx 5.09\ \text{units}[/tex]



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units to the right and 2 units
down?

Answers

Answer:

-2 = 3/6

Explanation:

6 units the right would be the X, and 2 units down would be the Y.

Answer:

y'' = 3/(x - 6)  - 2

Step-by-step explanation:

Given function

y = 3/x

Translation 6 units to the right:

f(x) → f(x - 6)y' = 3/(x - 6)

Translation 2 units down:

f(x) → f(x) - 2y'' = 3/(x - 6)  - 2

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Answer:

x < -3 or 2 < x < 7

Step-by-step explanation:

Due today answer with steps.

Answers

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Step-by-step explanation:

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Answers

Answer:

9

Step-by-step explanation:

18/2 = 9

27/3 =9

63 = 9

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answer 36

i HOPE IT'S HELP


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Step-by-step explanation:

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Answer:

A I think

Step-by-step explanation

Answer:

A

Step-by-step explanation:

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Answers

Answer:

i dont really get the question

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