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State the property that is used in each of the following state

Question

State the property that is used in each of the following statements $?$
If $a ∥ b,$ then $∠1 = ∠5$
If $∠4 = ∠6,$ then $a ∥ b$
If $∠4 + ∠5 = 18 0^{\circ},$ then $a ∥ b$

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State the property that is used in each of the following statements

?

a ∥ b,

then

∠1 = ∠5

∠4 = ∠6,

then

a ∥ b

∠4 + ∠5 = 18 0^{\circ},

then

a ∥ b

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Text solutionVerified

1.

a ∣∣ b

then

∠1 = ∠5

(corresponding angles)

2.

∠4 = ∠6

∠4 = ∠7

(corresponding angles)

∠4 = ∠6

(alternative angle)

3.

∠4 + ∠5 = 18 0^{o}

∠4 = ∠7

∠4 = 180 - ∠5

\Rightarrow ∠5 + ∠4 = 18 0^{o}

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Question Text	State the property that is used in each of the following statements $?$ If $a ∥ b,$ then $∠1 = ∠5$ If $∠4 = ∠6,$ then $a ∥ b$ If $∠4 + ∠5 = 18 0^{\circ},$ then $a ∥ b$
Answer Type	Text solution:1
Upvotes	150