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### Course: Integrated math 1>Unit 17

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 (~)
• congruent is things that are equal length, size etc. Two shapes that have the same proprtions (angles, sides etc) but are not necesarily the same size ( basically one is a scaled up version of the other)are similar. So an angle wih the sides 3, 4, and 5 will be similar to one with the sides of 6,, and 10, but not congruent.
(1 vote)
• What's the difference between similar and congruent?
(1 vote)
• For congruent shapes, they must be exactly the same shape.

For similar shapes, another shape can be obtained by enlarging or reducing the size of the shape.

For example, all circles are similar, since you can enlarge or reduce the size of the circle to obtain another circle.

Note that for shapes that are congruent, they are also similar.
• How would I solve this word problem: The perimeter of a square is 4 units greater than the combined perimeter of two congruent equilateral triangles. If the side length of the square is 10 units, what is the side length of the triangles?
(1 vote)
• First, you would have to find the perimeter of a square. Since each side length is 10, the perimeter is 10+10+10+10, or 40.

It says that the perimeter of the square is 4 units greater than the combined perimeter of the congruent equilateral triangles.

So, 40-4, or 36, is the total perimeter of both of the congruent equilateral triangles. Divide this by six to get each side of the triangle, since there are 6 equal sides in 2 congruent equilateral triangles.

36/6 is 6, so the side length of each side of the triangles is 6 units.

Does this make sense?
• What is the formula for a triangle
• Well there at a lot of formulas for a triangle
You have area, perimiter, missing angles, missing triangle lengths. Just google the one you want
(1 vote)
• Is the arrow symbol Sal draws commonly used in proofs? If so, what is the name of that symbol?
(1 vote)
• I assume you meant this =>

The symbol means "implies". For example, when I say p implies q (p => q), I mean "whenever p is true, q is true".

(1 vote)
• 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?