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Study with Quizlet and memorize flashcards containing terms like Given the two triangles below, are they necessarily congruent? Explain why or why not. A. No, AAA is not sufficient for congruence. One triangle might be larger than the other. B. No, AAA is not sufficient for congruence.
Study with Quizlet and memorize flashcards containing terms like Parallel Postulate, Parallel lines cut by transversal and alternate interior angles, Parallel lines cut by transversal and any pair of angles and more.
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance. In three-dimensional Euclidean space, a line and a plane that do not share a point are also said to be parallel. However, two noncoplanar lines are called skew lines.
No, parallel lines are not congruent. Two or more lines are parallel when they lie in the same plane and never intersect. They have the same slope. However, they may have different lengths. On the other hand, congruent lines are congruent to each other if they have the same length and lie in the same plane.
Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
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In advanced geometry lessons, students learn how to prove lines are parallel. More specifically, they learn how to identify properties for parallel lines and transversals and become fluent in constructing proofs that involve two lines parallel or not, that are cut by a transversal.
