Look at the parallelogram ABCD below.
What can be said about triangles ACD and ABD?
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Look at the parallelogram ABCD below.
What can be said about triangles ACD and ABD?
According to the side-angle-side theorem, the triangles are similar and coincide with each other:
AC = BD (Any pair of opposite sides of a parallelogram are equal)
Angle C is equal to angle B.
AB = CD (Any pair of opposite sides of the parallelogram are equal)
Therefore, all of the answers are correct.
All answers are correct.
True or false?
One of the angles in a rectangle may be an acute angle.
Congruent triangles have the same size and shape, but can be positioned differently! Triangle ABD can be rotated or reflected to match triangle ACD perfectly.
When triangles are congruent, they automatically have the same areas and perimeters, and they're also similar! Congruence is the strongest relationship - it includes all the others.
In parallelograms:
Yes! Both triangles share the diagonal AD as a common side. This shared side, plus the parallelogram properties, makes proving congruence much easier.
Absolutely! You could also use SSS (all three sides equal) since AC = BD, AB = CD, and AD = AD. The parallelogram gives you multiple ways to prove congruence.
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