You have this information about ΔABC, ΔDEF, and ΔGHI:AB = DF

AB = GI

BC = HI

DE = HI

m∠B = m∠D = m∠I

Which triangles must be congruent?
ΔABC and ΔDEF only

ΔGHI and ΔABC only

none of the triangles
ΔABC, ΔDEF, and ΔGHI

Answers

Answer 1

Answer: ΔABC, ΔDEF, and ΔGHI

I think all triangles are congruent. 2 sides and 1 angle of each triangle is has the same measure. Making these triangles congruent in SAS theorem.

Answer 2

Answer:

Answer: ΔABC, ΔDEF, and ΔGHI

Step-by-step explanation:

Given: In ΔABC, ΔDEF, and ΔGHI:

AB = DF AB = GI

BC = HI DE = HI

m∠B = m∠D = m∠I

In ΔABC and ΔGHI

AB = GI [given]

BC = HI [given]

m∠B = m∠I [given]

[ here m∠B and m∠I are the included angle of ΔABC and ΔGHI]

∴ ΔABC ≅ ΔGHI [by SAS congruence postulate]

In ΔABC and ΔDEF

AB = DF [given]

BC = DE [ Since BC = HI and DE = HI so by transitive property BC = DE]

m∠B = m∠D [given]

[ here m∠B and m∠D are the included angle of ΔABC and ΔDEF]

∴ ΔABC ≅ ΔDEF [by SAS congruence postulate]

Now, since ΔABC ≅ ΔGHI and ΔABC ≅ ΔDEF

⇒ ΔGHI ≅ ΔDEF [transitive property]

Hence, all the given triangles ΔABC, ΔDEF, and ΔGHI are con gruent to each other.

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Answers

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What is he reciprocal of 3

Answers

1/3 because reciprocal is the opposite

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One number is 5 times another. The sum of their reciprocals is 2/5. Determine the smaller number.

Answers

so x=5y
reciprocal of x=1/x then

sum of reciprocals means 1/x+1/y=2/5
subsitute x=5y for x in 1/x+1/y=2/5 and get
1/5y+1/y=2/5
multiply 1/y by 5/5 to make it 5/5y so you can add since the denomenators (bottom number) are the same

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What is the sum of the geometric series 2^0 + 2^1 + 2^2 + 2^3 + 2^3 + 2^4 + … + 2^9?

Answers

the nth term is
an=a1(r)^(n-1)
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the sum of a geometric seequence is
$S_(n)=(a_(1)(1-r^(n)))/(1-r)$
a1=1
r=2
we want to find $S_(10)$ (since we minus 1, the highest exponet is 9 so add 1 to make it correct)

$S_(10)=(1(1-2^(10)))/(1-2)$
$S_(10)=((1-1024)/(-1)$
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$S_(10)=1023$

Hello,

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How do you simplify 5^log5x

Answers

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Find the side of a square, whose area is equal to the area of a rectangle with sides 6.4m and 2.5m. Also find the perimeter of the square.

Answers

Answer:

side: 4 metres

perimeter: 16 metres

Step-by-step explanation:

Let's first find the area of this rectangle.

The area of a rectangle is denoted by A = lw, where l is the length and w is the width. Here, the length is l = 6.4 and the width is w = 2.5. Plug these in:

A = lw

A = 6.4 * 2.5 = 16 metres squared

We want to find the side of a square with area 16. Suppose the side length is x. The area of a square is denoted by A = x * x = x², so set this equal to 16:

x² = 16

x = √16 = 4

Thus, the side length is 4 metres.

The perimeter of a square is denoted by P = 4s, where s is the side length.

Here the side length is 4 metres, as we found, so:

P = 4s = 4 * 4 = 16

Hence the perimeter is 16 metres.

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