The reflection transformation in the question is a rigid transformation,
therefore, the image and the preimage are congruent.
The statements that are true are;
Reasons:
The given parameter are;
Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST
Required:
To select the true statements
Solution:
A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.
Therefore;
AB = RS
BC = ST
AC = RT
Given that the image formed by a reflection is congruent to the preimage, we have;
ΔABC ≅ ΔRST
∠ABC ≅ ∠RST
m∠ABC = m∠RST by the definition of congruency
∠BCA ≅ ∠STR
m∠BCA = m∠STR by the definition of congruency
∠BAC ≅ ∠SRT
m∠BAC = m∠SRT by the definition of congruency
Therefore, the true statements are;
- <u>AB = RS</u>; Image formed by rigid transformation
- <u>∠ABC ~ ∠RST</u>; Definition of similarity
- <u>ΔABC = ΔRST</u>; By definition of congruency
- <u>m∠BAC = m∠SRT</u>; by the definition of congruency
Learn more here:
brainly.com/question/11787764
Answer:
7/20
Step-by-step explanation:
Seventh grade: Total = 3 + 7 = 10
Number of boys = 7 boys
Probability of a boy being picked = 7/10
Eighth grade: Total 5 + 5 = 10
Number of boys = 5
Probability 5/10 = 1/2
The probability of the correct outcome = 7/10 * 1/2 = 7 / 20
Answer: 7 / 20
The surface area is 6075.96 in^3
Answer:
0.002
Step-by-step explanation:
cuz
The value of x in the given sector is determined as 7.1.
<h3>Area of the sector</h3>
Total area of the sector = area of the shaded + area of the unshaded
Since shaded and unshaded areas are equal, the value of x is calculated as follows;
πr²θ/360 = πx²60/360 + πx²60/360
πr²θ/360 = 2(πx²θ/360)
πr² = 2(πx²)
r² = 2x²
x² = r²/2
x² = (10²)/2
x² = 50
x = √50
x = 7.1
Thus, the value of x in the given sector is determined as 7.1.
Learn more about area of sector here: brainly.com/question/22972014
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