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$/_\ABC is an isosceles triangle. 6 . Given: /_5~=/_6 Prove: /_\ABC is an isosceles triangle. Proof: 335$

$6$ . $\triangle \mathrm{ABC}$ is an isosceles triangle. $6$ . $\newline$ $14$ . Given: $\angle 5 \cong \angle 6$ $\newline$ Prove: $\triangle A B C$ is an isosceles triangle. $\newline$ Proof: $\newline$ $335$

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Simplify complex fractions

Full solution

Q.

6

.

\triangle \mathrm{ABC}

is an isosceles triangle.

6

.

\newline

14

. Given:

\angle 5 \cong \angle 6

\newline

Prove:

\triangle A B C

is an isosceles triangle.

\newline

Proof:

\newline

335

Identify Given & Prove: Identify the given information and what needs to be proven. $\newline$ Given: \angle 5 \(\newlineot\approx \angle 6\), we need to prove that $\triangle ABC$ is an isosceles triangle.
Recall Isosceles Triangle: Recall the definition of an isosceles triangle. An isosceles triangle has at least two sides that are equal in length, which also means at least two angles are equal.
Use Given Information: Use the given information to relate it to the definition of an isosceles triangle. $\newline$ Since $\angle 5 \neq \angle 6$ , it means two angles in the triangle are congruent.
Determine Opposite Sides: Determine which sides are opposite to the congruent angles. $\newline$ The sides opposite to $\angle 5$ and $\angle 6$ must be equal in length because angles opposite to equal sides in a triangle are equal.
State Conclusion: State the conclusion based on the previous steps. $\newline$ Since the sides opposite to $\angle 5$ and $\angle 6$ are equal, triangle $ABC$ is an isosceles triangle.

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