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Math  /  Geometry

QuestionWhat else would need to be congruent to show that △ABC≅△DEF\triangle A B C \cong \triangle D E F by ASAA S A ? A. ∠C≅∠F\angle C \cong \angle F B. BC‾≅EF‾\overline{B C} \cong \overline{E F} C. AC‾≅OF‾\overline{A C} \cong \overline{O F} D. ∠A≅∠D\angle A \cong \angle D

Studdy Solution

STEP 1

1. We are given two triangles, △ABC\triangle ABC and △DEF\triangle DEF.
2. We want to show that these triangles are congruent using the Angle-Side-Angle (ASA) postulate.

STEP 2

1. Recall the ASA postulate for triangle congruence.
2. Identify the given congruent parts.
3. Determine the additional congruence needed.
4. Identify the correct option.

STEP 3

Recall the ASA postulate for triangle congruence:
The ASA postulate states that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

STEP 4

Identify the given congruent parts:
Assume we are given ∠B≅∠E\angle B \cong \angle E and AB‾≅DE‾\overline{AB} \cong \overline{DE}.

STEP 5

Determine the additional congruence needed:
To use the ASA postulate, we need another pair of congruent angles that are adjacent to the given congruent side AB‾≅DE‾\overline{AB} \cong \overline{DE}.

STEP 6

Identify the correct option:
The additional congruence needed is ∠A≅∠D\angle A \cong \angle D, which is adjacent to the side AB‾≅DE‾\overline{AB} \cong \overline{DE}.
Thus, the correct option is:
D.∠A≅∠D \boxed{D. \angle A \cong \angle D}

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