Questions: It is given that triangle DOG is congruent to triangle CAT. Determine who is correct. Cal says that triangle OGD is congruent to triangle CTA. Deb says that triangle ODG is congruent to triangle ATC. Ed says that triangle GDO is congruent to triangle TCA.

It is given that triangle DOG is congruent to triangle CAT. Determine who is correct.

Cal says that triangle OGD is congruent to triangle CTA.
Deb says that triangle ODG is congruent to triangle ATC.
Ed says that triangle GDO is congruent to triangle TCA.

Transcript text: It is given that $\triangle D O G \cong \triangle C A T$. Determine who is correct. Cal says that $\triangle O G D \cong \triangle C T A$. Deb says that $\triangle O D G \cong \triangle A T C$. Ed says that $\triangle G D O \cong \triangle T C A$.

Solution

Solution Steps

To determine who is correct, we need to check the order of vertices in the congruent triangles. Since $\triangle D O G \cong \triangle C A T$, the corresponding vertices are $D \leftrightarrow C$, $O \leftrightarrow A$, and $G \leftrightarrow T$. We will check each person's claim to see if the order of vertices matches the given congruence.

Step 1: Analyze the Given Congruence

We are given that $ \triangle DOG \cong \triangle CAT $. This implies that the corresponding vertices are matched as follows:

$ D \leftrightarrow C $
$ O \leftrightarrow A $
$ G \leftrightarrow T $

Step 2: Evaluate Cal's Claim

Cal claims that $ \triangle OGD \cong \triangle CTA $. The corresponding vertices based on Cal's claim would be:

$ O \leftrightarrow C $
$ G \leftrightarrow T $
$ D \leftrightarrow A $

Since the order does not match the original congruence, Cal's claim is incorrect.

Step 3: Evaluate Deb's Claim

Deb claims that $ \triangle ODG \cong \triangle ATC $. The corresponding vertices based on Deb's claim would be:

$ O \leftrightarrow A $
$ D \leftrightarrow T $
$ G \leftrightarrow C $

Again, the order does not match the original congruence, so Deb's claim is also incorrect.

Step 4: Evaluate Ed's Claim

Ed claims that $ \triangle GDO \cong \triangle TCA $. The corresponding vertices based on Ed's claim would be:

$ G \leftrightarrow T $
$ D \leftrightarrow C $
$ O \leftrightarrow A $

This order does not match the original congruence either, making Ed's claim incorrect as well.

Final Answer

All claims made by Cal, Deb, and Ed are incorrect. Thus, the final answer is: $\boxed{\text{All claims are incorrect}}$

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