Thank you for visiting In parallelogram ABCD one way to prove that diagonals and each other is to prove triangle AXB congruent to triangle CXD Which triangle congruency theorem. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
In a parallelogram, the Side Angle Side (SAS) congruency theorem is typically used to prove that diagonals bisect each other by showing two triangles formed by the diagonals are congruent.
Explanation:
In parallelogram ABCD, to prove that diagonals bisect each other, you could demonstrate that triangle AXB is congruent to triangle CXD. The correct triangle congruency theorem to prove this is typically the Side Angle Side (SAS) theorem if you have one angle and the two sides around it known to be equal.
The SAS rule states that if two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent. In the case of a parallelogram, the opposite sides are equal in length, and the diagonals bisect each other at an angle, making this the appropriate theorem.
Note that the HL (Hypotenuse Leg) theorem specifically applies to right triangles, which isn't necessarily the case in a generic parallelogram. The AAS (Angle Angle Side) theorem requires two angles and a side, and the SSS (Side Side Side) theorem requires all three sides.
Therefore, among the options given, SAS is the correct theorem to apply in proving that the diagonals of a parallelogram bisect each other when trying to establish the congruency of triangles AXB and CXD.
Learn more about Congruency Theorems here:
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