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QuestionIf △ABC≅△DEF\triangle ABC \cong \triangle DEF and AB=18,BC=10,AC=25AB=18, BC=10, AC=25, what is the length of DFDF? A. Cannot be determined B. 18 C. 10 D. 25

Studdy Solution

STEP 1

Assumptions1. Triangle ABC is congruent to triangle DEF. This means that their corresponding sides and angles are equal. . The length of side AB is18 units.
3. The length of side BC is10 units.
4. The length of side AC is25 units.
5. We are asked to find the length of side DF.

STEP 2

Since the two triangles are congruent, their corresponding sides are equal. This means that the length of side DF is equal to the length of its corresponding side in triangle ABC.

STEP 3

To find the corresponding side of DF in triangle ABC, we need to understand the order of the vertices in the congruence statement. In the congruence statement △ABC≅△DEF\triangle ABC \cong \triangle DEF, the order of the vertices tells us that vertex A corresponds to vertex D, vertex B corresponds to vertex, and vertex C corresponds to vertex F.

STEP 4

Therefore, side DF in triangle DEF corresponds to side AC in triangle ABC.

STEP 5

Since the corresponding sides of congruent triangles are equal, the length of side DF is equal to the length of side AC.
DF=ACDF = AC

STEP 6

Substitute the given value for the length of side AC into the equation.
DF=25DF =25The length of side DF is25 units. Therefore, the correct answer is D.25.

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