Question

If Δ C A T ≅ Δ D O G, which statement must be true?

A. m ∠ A = m ∠ O
B. m ∠ C = m ∠ G
C. CA = OG
D. ¯¯¯¯¯¯ C T ≅ ¯¯¯¯¯¯ D O

Answer 1

Answer:
`\angle{A}\cong\angle{O}`

Explanation:

Given :
`\triangle{CAT}\cong\triangle{DOG}`

We know that when two triangles are congruent then their corresponding sides and angles area also congruent.

So , if
`\triangle{CAT}\cong\triangle{DOG}`

Then,

`\angle{C}\cong\angle{D}\\\angle{A}\cong\angle{O}\\\angle{T}\cong\angle{G}`

And

`\overline{CA}\cong\overline{DO}\\\\\overline{AT}\cong \overline{DO}\\\\\overline{CT}\cong \overline{DG}`

Hence, from the given options the true statement is
`\angle{A}\cong\angle{O}`

Answer 2

A. m∠A = m∠O

Explanation:

`\triangle CAT\cong\triangle DOG\\\\\text{Therefore:}\\\\\angle C\cong\angle D\\\angle A\cong\angle O\\\angle T\cong\angle G\\CA\cong DO\\CT\cong DG\\AT\cong OG`