Proving Triangle Congruence and Similarity

Now we know about different kinds of triangles and their characteristics, so we should be able to look at two triangles and say whether they are similar, congruent, or unrelated. For more information on what that means and how to do it, check out this clip! It's chock-full of theorems.
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[@Rushan_sk]

(Please pin this comment)
Key Points of the Video:
00:02 Geometry involves proving things using logic.
00:43 Triangles can be similar or congruent
01:17 Proving triangle similarity with proportional sides or identical angles
01:43 Triangles must be similar regardless of side lengths
02:14 Triangle congruence and similarity explained
02:43 Hypotenuse-leg and angle side angle theorems
03:12 Proving triangles congruence and similarity.
03:45 Proving triangle congruence and similarity is essential for calculating information about triangles.

[@FrancescoDiSiena]

he didn't pin it (i think you are 6 years late)

[@kripashankarshukla4073]

Sir congratulations for 100K subscribers. Now I am sure that all my friends have subscribed you. Thank you sir for your video

[@namon2287]

Professor Dave, please please make a video on Law of Definite Proportions and Law of Multiple Proportions. It's a relatively difficult mathematical concept in chemistry to understand AT FIRST, and many people would be lucky to see how you explain first (because you are awesome!!)

[@ProfessorDaveExplains]

i talk about those in my clip about the history of atomic theory!

[@theguythatdoesmath9863]

What about the ASS theorem?
(idk if that exists, but it might, and im too lazy to find out)

[@NoActuallyGo-KCUF-Yourself]

That's known as the ambiguous case - i.e. there could be two solutions.

[@drosha9314]

thank you professor dave

[@ultrainferno9025]

Who else is watching this because your school gave it for you to watch

[@irodaikromxonova9556]

Thank you Professor!

[@Sccoropio]

professor dave could you please post all the slides used in this playlist somewhere?

[@anuragtiwari2270]

Happy diwali sir.. one of major festival of India

[@FrancescoDiSiena]

writing down everything in this episode hurt my hand

[@OPTIONALWATCH]

What about to prove if two figures are similar but not congruent?

[@carultch]

You simply need to prove that two out of 3 of the angles are identical, and then you prove that triangles are similar. Or prove that enough of the side lengths, come in proportion to each other.

[@matthewcecil8552]

My first, first comment.

[@yatishsharma6987]

Nyc vedio

[@Digitalbandits99]

What if side-side-angle are same?
I guess if two sides are same then there should be only one angle that touch both these sides ...

[@Rng_killer2324]

where the ASS

[@NoActuallyGo-KCUF-Yourself]

1:26 - Those are not triangles; they are lines. But I guess it is technically correct to say that all lines are similar to each other.

[@ProfessorDaveExplains]

Triangles are not lines. I have no idea what you're saying.

[@Aleggbriel1]

Does the hypotenuse- Leg Theorem work for non right triangles?

[@Carrymejane]

Nope, it has it own formula for different triangles

[@JakeLinAu]

Great videos!😃

[@ReimskyToussaint]

Is it now formally accepted to use/say "equal" where "congruent" is traditionally expected? Or is it to benefit students. I am also both a loved of learning and teacher. Would appreciate some feedback.
(Also, this is nitpicking, but I would stretch that 30-60-90 ∆ sketch horizontally a bit for a more accurate representation)
Thanks for your videos.

[@carultch]

The reason we say congruent instead of equal, is that the triangles could be flipped, rotated, moved, applied to different parts of a figure, and all sorts of variations. Congruent simply specifies equality in the context that geometry cares about, when comparing shapes of the same type, size, ratios, and angles.

[@NoActuallyGo-KCUF-Yourself]

No, that is not at all accepted. Congruent and equal are different. Equal or equivalent means same magnitude or value. Congruent means same size (equivalent) and same shape (similar) simultaneously.
Two triangles can be equal to each other but be neither similar nor congruent.

[@fullerz6147]

aha the old intro

[@vvajay]

Apparently, Hypotenuse-Leg is same as SAS, as the angle is 90 degrees

[@NoActuallyGo-KCUF-Yourself]

No, H-L is a special case of SSA, not SAS.

[@Gigiwithlove_x]

thanks fo this

[@ta_ogboy9998]

So if any 2 angles and 1 side, 3 sides, or a leg and a hypotnuese of a right triangle are the same, they are congruent?