All categories

2 years ago

Using Rigid motion, explain in detail, why triangle ABC must be congruent to triangle DEF

1 answer:

7 0

Using rigid motion, both of these triangles will be congruent. The reason is because rigid motions include reflections, translations, and rotations.

None of these transformations will affect the size or shape of the figure, therefore keeping them congruent.

You might be interested in

Choose one of the squares facts from problem 1?

egoroff_w [7]

I think you forgot to put in the image

8 0

2 years ago

<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

2 years ago

Don’t mind the blue tete

jeka94

Your answer is gonna be C.

5 0

3 years ago

The confidence interval is to .

navik [9.2K]

Answer:

See below

Step-by-step explanation:

The purpose of the confidence interval is to give a range of where the true value of a parameter lies given a confidence level.

8 0

2 years ago

Antoine went on vacation to Las Vegas. His room cost $115.62 each night. His flight there cost $45.70 and his flight home was $3

uysha [10]

The total amount is the sum of the cost of three nights in the hotel, $346.86, the flight costs, $45.70 + $32.49 = $78.19, and four days of food, $60, the amount he lost, $25, less the amount he won, $75. Calculating,
($346.86 + $78.19 + $60 + $25) - ($75) = $435.05

3 0

3 years ago

Read 2 more answers