Mathematics: Find the percent of increase from 28 songs to 57 songs. Round to the nearest tenth of a percent if necessary.

Find the percent of increase from 28 songs to 57 - id285710454978, bbyitskeke1242

victoriadorvilu

22.10.2022

Option B is correct.

Statement: ∠AFE ≅ ∠AFD

Reason: Transitive Property of Equality

Explanation:

Given that:

$\overline{BC} || \overline{DE}$ and $\angle GAC \cong \angle AFD$

Prove that : $\overleftrightarrow{GH} \perp \overleftrightarrow{DE}$

Proof:

Given:

$\angle GAC \cong \angle AFD$ ....[1]

By theorem of corresponding angles:

For parallel lines cut by transversal , the corresponding angles are congruent.

then;

$\angle GAC \cong \angle AFE$ ....[2]

Transitive property of equality states that if x = y and y = z then; x = z

Using transitive property of equality in [1] and [2] we have;

$\angle AFE \cong \angle AFD$

By Linear pair theorem states that if the two pairs are adjacent to each other then they are supplementary.

⇒ $\angle AFD$ and $\angle AFE$ are supplementary.

We know that:

If two congruent angles are supplementary, then each angle is of right angle i.,e 90 degree

⇒ $m\angle AFD =m\angle AFE = 90^{\circ}$

By definition of perpendicular line:

If two line meet at a right angle i.,e 90 degree, then those lines are perpendicular.

⇒ $\overleftrightarrow{GH} \perp \overleftrightarrow{DE}$ Hence proved!

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