congruent - SSSAnswer by Arteom, Friday December 10, 2010
This sentence can be complete as: After a congruence transformation the area of a triangle would be the same as it was before.
A ruler or a compass would help or aternatively use Pythagoras' theorem to prove that the diagonals are of equal lengths
That would be a postulate
SSS is enough to show congruence.
Excuse me, but two triangles that have A-A-S of one equal respectively to A-A-S of the other are not necessarily congruent. I would love to see that proof!
The ASS postulate would be that:if an angle and two sides of one triangle are congruent to the corresponding angle and two sides of a second triangle, then the two triangles are congruent.The SSA postulate would be similar.Neither is true.
We cannot determine without seeing the data for PRS & QRS. My guess though would be ASA Though it could also be SSS
Theorem: A Proven Statement. Postulate: An Accepted Statement without Proof. They mean similar things. A postulate is an unproven statement that is considered to be true; however a theorem is simply a statement that may be true or false, but only considered to be true if it has been proven.
I'm happy to help! Please provide the paragraph or the statement you would like me to complete.
You would use the AA Similarity Postulate to prove that the following two triangles are similar. True or false?
congruent - SSSAnswer by Arteom, Friday December 10, 2010
Yes, he must have proved his own Theorem otherwise it would not have been adopted by mathematicians across the globe. I'm sure you could test out the theorem: check whether c2 really does equal b2 + a2 in a manual measurement of a triangle; though this is less accurate and not as precise as the Theorem.
Recall that two triangles are similar if one is simply a larger or smaller version of the other. So if you can make one bigger or smaller (this is called dilating) so that it looks exactly the same as another (and would fit exactly if moved with a congruence transform), then this would show similarity.
This sentence can be complete as: After a congruence transformation the area of a triangle would be the same as it was before.
A ruler or a compass would help or aternatively use Pythagoras' theorem to prove that the diagonals are of equal lengths
Not in general. Imagine making a pentagon out of sticks connected with hinges for the vertexes. You can bend it all around, making pentagons that are not congruent to the original, even though the sides remain the same length. A similar triangle would be rigid, even if the corners were connected with hinges.