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1 year ago

How are rigid transformations used to justify the SAS congruence theorem?

2 answers:

6 0

Rigid transformations preserve segment lengths and angle measures. If you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. To prove SAS, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. Then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the SAS congruence theorem.

skelet666 [1.2K]1 year ago

3 0

<span>Rigid transformations (translations, reflections and rotations) are transformations that maintain the measure of line segments and angles. Being able to map a pre-image to an image using rigid transformations means that the sides are the same length, as is the angle between the two.</span>

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A musician begins performing concerts. His first concert had 500 people attending. The musician says that if attendance grows by

Mashutka [201]

Answer:551.25

Step-by-step explanation:

500 x .05 =25+500= 525 which is the second concert. Multiply that by .05 which is 26.25, add that to 525 to get 551.25 which is not 650.

7 0

1 year ago

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If clare doesn't

AVprozaik [17]

We have been given that Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount 1.03.

We are asked to write an expression for the amount of money Clare would have after 30 years if she never withdraws money from her account.

We will use exponential growth function to solve our given problem.

An exponential growth function is in form $y=a(1+r)^x$ , where

y = Final value,

a = Initial value,

r = Growth rate in decimal form,

x = Time.

$3\%=\frac{3}{100}=0.03$

We can see that initial value is $160. Upon substituting our given values in above formula, we will get:

$y=160(1+0.03)^x$

$y=160(1.03)^x$

To find amount of money in Clare's account after 30 years, we need to substitute $x=30$ in our equation.

$y=160(1.03)^{30}$

Therefore, the expression $160(1.03)^{30}$ represents the amount of money that Clare would have after 30 years.

8 0

2 years ago

A farmer plans to create a rectangular garden that he will enclose with chicken wire. The garden can be no more than 30 ft wide.

andrew-mc [135]

P is the perimeter of a rectangular garden.
P = 2 L + 2 W,
where L is the length and W is the width of a rectangle.
W ≤ 30 ft
2 L + 2 W ≤ 180 ft
2 ( L + W ) ≤ 180
L + W ≤ 180 / 2
L + W ≤ 90
Answer:
A system of inequalities:
W ≤ 30
L + W ≤ 90

4 0

2 years ago

Find a rational number halfway between 7/8 and 6/7

algol [13]

<h3>Answer: 97/112</h3>

================================================

How to get this answer:

Midpoint formula: (A+B)/2 = C

A and B are the endpoints with C as the midpoint

A = 7/8

B = 6/7

A+B = 7/8 + 6/7

A+B = 49/56 + 48/56

A+B = (49+48)/56

A+B = 97/56

(A+B)/2 = (97/56) divided by 2

(A+B)/2 = (97/56) times (1/2)

(A+B)/2 = (97*1)/(56*2)

(A+B)/2 = 97/112

8 0

2 years ago

Amee received an end of year bonus of $1550 at work and went on a shopping spree. She spent $225 at the department store, $275 a

atroni [7]

Answer: She has $1022 left.

Step-by-step explanation:

The total amount that Amee received an the end of year as bonus at work is $1550.

She went on a shopping spree, spending $225 at the department store, $275 at the home furnishing store, and $28 at the card shop. Therefore, the total amount that she spent at the department store, the home furnishing store, and the card shop is

225 + 275 + 28 = $528

Therefore, the total amount of her bonus that she has left is

1550 - 528 = $1022

6 0

2 years ago