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"Ankita wants to prove " DeltaABC ~= De...

`"Ankita wants to prove " DeltaABC ~= Delta DEF " using " SAS. She " knows " `AB = DE and AC = DF`. "What additional piece of information does she need ?" `

A

`angle A = angle D`

B

`angle C = angle F`

C

`angle B = angle E`

D

`angle A = angle B`

Text Solution

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The correct Answer is:
To prove that triangle ABC is congruent to triangle DEF using the Side-Angle-Side (SAS) rule, Ankita already knows two sides: 1. \( AB = DE \) 2. \( AC = DF \) To apply the SAS rule, she needs one additional piece of information, which is the angle included between the two sides. Specifically, she needs to know that the angle \( \angle A \) in triangle ABC is equal to the angle \( \angle D \) in triangle DEF. ### Step-by-Step Solution: 1. **Identify the given information**: - \( AB = DE \) - \( AC = DF \) 2. **Recall the SAS rule**: - The SAS rule states that if two sides of one triangle are equal to two sides of another triangle, and the angles included between those sides are equal, then the two triangles are congruent. 3. **Determine the missing information**: - The angle that is included between the sides \( AB \) and \( AC \) in triangle ABC is \( \angle A \). - The angle that is included between the sides \( DE \) and \( DF \) in triangle DEF is \( \angle D \). 4. **Conclude the requirement**: - To prove triangle ABC is congruent to triangle DEF using the SAS rule, Ankita needs to show that: \[ \angle A = \angle D \] ### Final Answer: Ankita needs the additional information that \( \angle A = \angle D \). ---
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