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Answer:
AC is perpendicular to BD
Step-by-step explanation:
Given a triangle ABD. C is the mid point of BD.
To prove that the two triangles are congruent we have to use SAS axiom.
Here consider two triangles ABC and ADC
Statement Reason
1) BC = CD D is the mid point of BD
2) AC = AC Reflexive property
Since we have two sides congruence we must have included angle congruence
i.e. Angle ACB = Angle ACD
If this information is given, then this completes the SAS congruence for the two triangles ABC and ADC
Hence answer is
the information that AC is perpendicular to BD is sufficient to complete the proof.
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Rewritten by : Barada
The SAS congruence postulate requires two sides and an included angle of one triangle to respectively match two sides and an included angle of another triangle. Even for right triangles, this applies, and knowledge of the Pythagorean theorem can be helpful in understanding this
To prove that two triangles are congruent using the Side-Angle-Side (SAS) congruence postulate, you need to ensure that two sides and the angle between them in one triangle correspond respectively to two sides and the angle between them in the other triangle.
The criteria for the SAS postulate can be fulfilled involving any triangle, including a right triangle. From the context of the right triangles in the question, one should understand Pythagorean theorem (a² + b² = c²) where 'a' and 'b' are the lengths of the other two sides and 'c' is the length of the hypotenuse. That said, knowing two sides of each triangle and the included angle is enough to apply SAS congruence postulate.
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