MATHEMATICS MIDDLE SCHOOL

Two right triangles on a coordinate plane are similar but not congruent.Each of the legs of both triangle are extended by 1 unit,creating two new right triangles.Are the resulting triangles similar? explain using an example

Answers

Answer 1
Answer:
Virtually every time you try this stunt, the new triangles
are NOT similar.

Example:

Triangle A₀ . . . legs = 3 and 4;  hypotenuse = √25  = 5 .
Triangle B₀ . . . legs = 6 and 8;  hypotenuse = √100 = 10 .

Ratio of short legs = 6/3 = 2
Ratio of long legs  = 8/4 = 2
Ratio of hypotenuses = 10/5 = 2
The triangles are similar. 

Add 1 unit to all legs:

Triangle A₁ . . .  legs = 4 and 5;  hypotenuse = √41
Triangle B₁ . . .  legs = 7 and 9;  hypotenuse = √130

Ratio of short legs = 7/4 = 1.75
Ratio of long legs  = 9/5 = 1.8
Ratio of hypotenees = √(130/41) = 1.78 .

New triangles are NOT similar.

I think this ONLY works when the original triangles are
congruent, so the ratio of their similarity is 1:1. 
When each leg of both triangles is extended by the same
amount, they are still congruent.
 
But the question stipulates that they are NOT congruent.
So the answer to the question is:   No.  Never.
 
Answer 2
Answer: They are similar, by SSS. This shows that the sides are all similar but may not be congruent. And they started out similar, and they have the same scale factor. If you had one more angle besides the 90, you would be able to figure out the angles inside and have AA to justify. 
Sorry if this is a bad explanation. 

Related Questions

Is 0.111... a repeating decimal, terminating decimal, or neither?
Write an algebraic expression to represent the cost of a concert ticket,h,with a service charge of $6.75.
There were 2.4 cups of water in Barkley's waterdish. He drank 1.33 cups. How much water is still inthe water dish?
If 1/4 of X is 16 what is 3/4 of x
Emily paid 287.50 in taxes to the school. This years taxes were 15% increase from last year. What did Emily pay?

Which of the following illustrates the truth value of the given conditional statement?If 6 • 3 = 18, then 4 + 8 = 20.

Answers

Answer:

6x3

Step-by-step explanation:

sorry if wrong

Solve the equation for y.

8x – 9y = 11

Answers


Watch carefully:

                                             8x - 9y = 11

Add  9y  to each side:                    8x = 11 + 9y

Subtract  11  from each side:    8x - 11 = 9y

Divide each side by  9 :        y = 1/9 of (8x - 11)


8x-9y=11subtract 8x from both sides-9y= -8x+11divide both sides by -9y= 8/9x-11/9hope this helps

HI CAN I PLEASE GET SOME HELP PLEASE THANK YOU WICH OF THE FOLLOWING IS EQUIVALENT TO THE EXPRESSION BELOW? Square root of -169 A)13i B)-13 C)13 D)-13i

Answers

Answer:

The answer would be A 13i

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

√(-169)=i√(169) =13i

If x^(2) - 2 = 2^(2/3) + 2(-2/3) prove that x = 2^(1/3)+2^(-1/3)

Answers

Step-by-step explanation:

x² - 2 = 2^(2/3) + 2^(-2/3)

x² = 2^(2/3) + 2 + 2^(-2/3)

x² = (2^(1/3))² + 2 × 2^(1/3) × 2^(-1/3) +

(2^(-1/3))² (It is in the form of a²+2ab+b²)

x² = (2^(1/3) + 2^(-1/3))²

x = 2^(1/3) + 2^(-1/3)

cassie draws 1 line to cut a square into two smaller shapes. which could NOT be the two smaller shapes?

Answers

They could ONLY be triangles, rectangles, or nameless quadrilaterals. They couldn't be anything else.
trapezoids because no matter what way you place them it can not make a square

Which number has the greatest value? A) 3.5
B) 15
C) 1 16
D) 26 100

Answers

D. 26,100 I believe is your answer
Other Questions
Andrew's recipe requires 7 pieces of toast every 14 spoons of butter.how many pieces of toast will he need if he uses 22 spoons of butter?
Is 1000 feet greater than 300 yrs
Why is the mean not affected by very high or low values in the data?
PLEASE HELP!! QUICKKK!Mark proofread 15 pages in 2 hours for $40What Is her proofreading rate in pages per hour?how much does she receive on average for a page?