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$Use the given information to prove that /_\HFG~=/_\EFD. Given: bar(GD) bisects bar(HE) Send To Proof {:[ bar(HE)_|_ bar(HG)],[ bar(HE)_|_ bar(ED)]:} Send To Proof Send To Proof Prove: /_\HFG~=/_\EFD quad Send To Proof Statement Reason 1 ◻ Reason? Validate$

Use the given information to prove that $\triangle H F G \cong \triangle E F D$ . $\newline$ Given: $\overline{G D}$ bisects $\overline{H E}$ $\newline$ Send To Proof $\newline$ $\begin{array}{l} \overline{H E} \perp \overline{H G} \\ \overline{H E} \perp \overline{E D} \end{array}$ $\newline$ Send To Proof $\newline$ Send To Proof $\newline$ Prove: $\triangle H F G \cong \triangle E F D \quad$ Send To Proof $\newline$ Statement $\newline$ Reason $\newline$ $1$ $\square$ Reason? $\newline$ Validate

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Math Problems

Algebra 1

Transformations of absolute value functions: translations and reflections

Full solution

Q. Use the given information to prove that

\triangle H F G \cong \triangle E F D

\newline

Given:

\overline{G D}

bisects

\overline{H E}

\newline

Send To Proof

\newline

\begin{array}{l} \overline{H E} \perp \overline{H G} \\ \overline{H E} \perp \overline{E D} \end{array}

\newline

Send To Proof

\newline

Send To Proof

\newline

Prove:

\triangle H F G \cong \triangle E F D \quad

Send To Proof

\newline

Statement

\newline

Reason

\newline

1

\square

Reason?

\newline

Validate

Draw Triangles $HFG$ and $EFD$ : Draw triangles $HFG$ and $EFD$ .
Use Segment Bisector Property: Since $\overline{GD}$ bisects $\overline{HE}$ , we know that $\overline{HD}$ is congruent to $\overline{DE}$ .
Identify Right Angles: $\overline{HE}$ is perpendicular to $\overline{HG}$ , so $\angle HEG$ is a right angle.
Establish Angle Congruence: $\overline{HE}$ is also perpendicular to $\overline{ED}$ , so angle $HED$ is a right angle.
Apply Reflexive Property: Since both angles $HEG$ and $HED$ are right angles, they are congruent.
Apply AAS Congruence Theorem: By the Reflexive Property, $\overline{GD}$ is congruent to itself.
Apply AAS Congruence Theorem: By the Reflexive Property, $\overline{GD}$ is congruent to itself.Triangles $HFG$ and $EFD$ have two angles congruent and a side congruent (angle-angle-side), so by the AAS Congruence Theorem, the triangles are congruent.