Holden tried to prove that $ riangle F G H \cong riangle F I H$.
\begin{tabular}{lll}
& Statement & Reason \
\hline 1 & $\overline{I H} \cong \overline{G H}$ & Given \
2 & $\overline{F H} \cong \overline{F H}$ & Line segments are congruent to themselves. \
3 & $ riangle F G H \cong riangle F I H$ & Side-side congruence
\end{tabular}

What is the first error Holden made in his proof?

Choose 1 answer:
(A) Holden used an invalid reason to justify the congruence of a pair of sides or angles.
(B) Holden only established some of the necessary conditions for a congruence criterion.
(c) Holden established all necessary conditions, but then used an inappropriate congruence criterion.
(D) Holden used a criterion that does not guarantee congruence.

Question

Holden tried to prove that $	riangle F G H \cong 	riangle F I H$.
\begin{tabular}{lll} 
& Statement & Reason \
\hline 1 & $\overline{I H} \cong \overline{G H}$ & Given \
2 & $\overline{F H} \cong \overline{F H}$ & Line segments are congruent to themselves. \
3 & $	riangle F G H \cong 	riangle F I H$ & Side-side congruence
\end{tabular}

What is the first error Holden made in his proof?

Choose 1 answer:
(A) Holden used an invalid reason to justify the congruence of a pair of sides or angles.
(B) Holden only established some of the necessary conditions for a congruence criterion.
(c) Holden established all necessary conditions, but then used an inappropriate congruence criterion.
(D) Holden used a criterion that does not guarantee congruence.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To identify the first error in Holden's proof, we must examine the statements and reasons provided in the proof. ‖ ‖ step 2 ⋮ The first statement is that $\overline{IH} \cong \overline{GH}$, with the reason given as "Given". This is a valid statement and reason. ‖ ‖ step 3 ⋮ The second statement is that $\overline{FH} \cong \overline{FH}$, with the reason "Line segments are congruent to themselves". This is also a valid statement and reason. ‖ ‖ step 4 ⋮ The third statement claims that $ riangle FGH \cong riangle FIH$ based on "Side-side congruence". However, there is no such congruence criterion as "Side-side congruence". The correct criteria are Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles. ‖ ‖ step 5 ⋮ Since Holden has only shown two sides to be congruent and has not established the congruence of the third side or any angles, he has not satisfied any of the valid congruence criteria. ‖ ∻1 Answer∻ ***D*** ∻Key Concept∻ ⚹Triangle Congruence Criteria⚹ ∻Explanation∻ ⚹To prove two triangles congruent, one must satisfy one of the valid congruence criteria: SSS, SAS, ASA, AAS, or HL for right triangles. "Side-side congruence" is not a recognized criterion.⚹◊What is the formula for calculating the area of a triangle using the side-side-side congruence criterion?⍭ Generate me a similar question◊

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