Find the area, circumference =6pi yd
1 answer:
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Answer:
1) c ║ d by consecutive interior angles theorem
2) m∠3 + m∠6 = 180° by transitive property
3) ∠2 ≅ ∠5 by definition of congruency
4) t ║ v Corresponding angle theorem
5) ∠14 and ∠11 are supplementary Definition of supplementary angles
6) ∠8 and ∠9 are supplementary Consecutive interior angles theorem
Step-by-step explanation:
1) Statement Reason
m∠4 + m∠7 = 180° Given
m∠4 ≅ m∠6 Vertically opposite angles
m∠4 = m∠6 Definition of congruency
m∠6 + m∠7 = 180° Transitive property
m∠6 and m∠7 are supplementary Definition of supplementary angles
∴ c ║ d Consecutive interior angles theorem
2) Statement Reason
m∠3 = m∠8 Given
m∠8 + m∠6 = 180° Sum of angles on a straight line
∴ m∠3 + m∠6 = 180° Transitive property
3) Statement Reason
p ║ q Given
∠1 ≅ ∠5 Given
∠1 = ∠5 Definition of congruency
∠2 ≅ ∠1 Alternate interior angles theorem
∠2 = ∠1 Definition of congruency
∠2 = ∠5 Transitive property
∠2 ≅ ∠5 Definition of congruency.
4) Statement Reason
∠1 ≅ ∠5 Given
∠3 ≅ ∠4 Given
∠1 = ∠5 Definition of congruency
∠3 = ∠4 Definition of congruency
∠5 ≅ ∠4 Vertically opposite angles
∠5 = ∠4 Definition of congruency
∠5 = ∠3 Transitive property
∠1 = ∠3 Transitive property
∠1 ≅ ∠3 Definition of congruency.
t ║ v Corresponding angle theorem
5) Statement Reason
∠5 ≅ ∠16 Given
∠2 ≅ ∠4 Given
∠5 = ∠16 Definition of congruency
∠2 = ∠4 Definition of congruency
EF ║ GH Corresponding angle theorem
∠14 ≅ ∠16 Corresponding angles
∠14 = ∠16 Definition of congruency
∠5 = ∠14 Transitive property
∠5 + ∠11 = 180° Sum of angles on a straight line
∠14 + ∠11 = 180° Transitive property
∠14 and ∠11 are supplementary Definition of supplementary angles
6) Statement Reason
l ║ m Given
∠4 ≅ ∠7 Given
∠4 = ∠7 Definition of congruency
∠2 ≅ ∠7 Alternate angles
∠2 = ∠7 Definition of congruency
∠2 = ∠4 Transitive property
∠2 ≅ ∠4 Definition of congruency
∠2 and ∠4 are corresponding angles Definition
DA ║ EB Corresponding angle theorem
∠8 and ∠9 are consecutive interior angles Definition
∠8 and ∠9 are supplementary Consecutive interior angles theorem.
Option a: is the equivalent expression.
Explanation:
The expression is where
Let us simplify the expression, to determine which expression is equivalent from the four options.
Multiplying the powers, we get,
Cancelling the like terms, we have,
This equation can also be written as,
Multiplying the terms in denominator, we have,
Thus, the expression which is equivalent to is
Hence, Option a is the correct answer.