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## High school geometry

### Course: High school geometry>Unit 3

Lesson 1: Transformations & congruence

# Angle congruence equivalent to having same measure

Two angles are congruent if and only if they have the same measure.

## Want to join the conversation?

• Hello, is there a difference between Congruent and Equivalent? •  Congruent is a term specific to geometry. Two figures are congruent when you can map one perfectly onto the other by reflection, rotating, and translating it without distortion.

Equivalent is a more general term. In general, it means 'the same as, in all relevant ways.' In the context of the video title 'Angle congruence equivalent to having same measure', it means that the sentence "These angles are congruent" is true exactly when "These angles have the same measure" is true.

That is, if these angles are congruent, then they have the same measure. And if they are not congruent, then they have different measures.
• At , what's "prime"? When would we see that? And how would we write that? • This is a second meaning of prime in math, like in the transformers movies (Optimus Prime). It is an indication of a point that has been moved by one of the transformation (translation, rotation, reflection, or dilation) and is represented as A' B' or C'. So the original point A is moved to A', the original point B is moved to B', and the original point C is moved to C'.
You could even do two transformations on a point and end up with A double prime A".
• so does congruent (≅) mean both equal (=) and similar (~) • Are ∠ABC and ∠DEF congruent even if the lengths of AB and DE are not equal, if they have the same measure?

Or is it ambiguous and depends on the problem?
(1 vote) • What is the formula for a triangle • What is the => thing that he drew? • what is the formula for finding triangle • According to Wikipedia, "In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.[self-published source]

The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation.[citation needed] Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections.

Any object will keep the same shape and size after a proper rigid transformation.

All rigid transformations are examples of affine transformations. The set of all (proper and improper) rigid transformations is a mathematical group called the Euclidean group, denoted E(n) for n-dimensional Euclidean spaces. The set of proper rigid transformations is called special Euclidean group, denoted SE(n).

In kinematics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies. According to Chasles' theorem, every rigid transformation can be expressed as a screw displacement." 