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3 years ago

How can you use isometries to prove congruence theorems?

Mathematics

1 answer:

arsen [322]3 years ago

8 0

Answer:

I think this is what your asking

Step-by-step explanation:

Isometries are sometimes also called congruence transformations. Two figures that can be transformed into each other by an isometry are said to be congruent (Coxeter and Greitzer 1967, p. ... If a plane isometry has more than one fixed point, it must be either the identity transformation or a reflection.

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Find the area of a rectangle that is 7 cm long and 3 cm wide. You can use the tool to help you solve. 7 cm2 10 cm2 20 cm2 21 cm2

stiks02 [169]

Answer:

21sq

Step-by-step explanation:

multiply the l times the w which would be 3x7 and get 21.

8 0

3 years ago

The length of a rectangle is 8 in. more than its width. The perimeter is 52 in. What is the length of the rectangle?

Levart [38]

$L=w+8 \\\\ P=2L+2w \\ P=52in \\\\ 2(w+8)+2w=52 \\\\ 2w+16+2w=52 \\\\ 4w=52-16 \\\\ 4w=36 \\\\ \boxed{w=\frac{36}{4}=4in} \\\\ L=4+8 \\\\ \boxed{L=12in}$

8 0

3 years ago

Read 2 more answers

What is the area of this figure?

Dimas [21]

A = (16 * 9) + 1/2(16+31)(15) + 1/2(20)(31)
A = 144 + 352.5 + 310
A = 806.5

answer is A
806.5

6 0

4 years ago

From Euler’s relation eiθ = cosθ + isinθ,

adelina 88 [10]

Answer:

(a) The graphic representation is in the attached figure.

(b) $\cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$ .

(c) $\sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}$ .

Step-by-step explanation:

(a) Given a complex number $e^{i\theta}$ we know, from Euler's formula that $e^{i\theta} = \cos(\theta)+i\sin(\theta)$ . So, it is not difficult to notice that

$|e^{i\theta}|^2 = \cos^2(\theta)+\sin^2(\theta) =1$

so it is on the unit circumference. Also, notice that the Cartesian representation of the complex number is $(\cos(\theta), \sin(\theta))$ .

Now,

$e^{-i\theta} = \cos(\theta)+i\sin(-\theta) = \cos(\theta)-i\sin(\theta)$ .

Notice that $e^{-i\theta}$ has the same modulus that $e^{i\theta}$ , so it is on the unit circumference. Beside, its Cartesian representation is $(\cos(\theta), -\sin(\theta))$ .

So, the points $(\cos(\theta), \sin(\theta))$ and $(\cos(\theta), -\sin(\theta))$ are symmetric with respect to the X-axis. All this can be checked in the attached figure.

(b) Notice that

$e^{i\theta} + e^{-i\theta} = \cos(\theta)+i\sin(\theta) + \cos(\theta)-i\sin(\theta) = 2\cos(\theta)$

Then,

$\cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$ .

(c) Notice that

$e^{i\theta} - e^{-i\theta} = \cos(\theta)+i\sin(\theta) - \cos(\theta)+i\sin(\theta) = 2i\sin(\theta)$

Then,

$\sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}$ .

7 0

3 years ago

Isabella's mother has a garden with a total area of 10 2 3 square feet. She plans her planting season like this: 1 4 of the gard

kkurt [141]

I am going to use the following numbers for the calculations.
10 2/3 square feet, 1/4 peas, and 3/4 corn.

Area with peas:

You need to find out what 1/4 of the total area is.

1/4 x 10 2/3
1/4 x 32/3
1/1 x 8/3
Area with peas is 8/3 or 2 2/3 square feet.

Area with corn:
You will find out what 3/4 of the total area is.

3/4 x 10 2/3
3/4 x 32/3
1/1 x 8/1
The area with corn is 8 square feet.

6 0

3 years ago