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## Praxis Core Math

### Unit 1: Lesson 5

Geometry- Properties of shapes | Lesson
- Properties of shapes | Worked example
- Angles | Lesson
- Angles | Worked example
- Congruence and similarity | Lesson
- Congruence and similarity | Worked example
- Circles | Lesson
- Circles | Worked example
- Perimeter, area, and volume | Lesson
- Perimeter, area, and volume | Worked example

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# Congruence and similarity | Worked example

Sal Khan works through a question on triangle congruence from the Praxis Core Math test.

## Want to join the conversation?

- where can I get more practic with this?(5 votes)
- You can look earlier in this lesson for some practice questions as well as terminology and definitions.

Hope this helps!

-Nova(4 votes)

- How do i know when to use SSS,SAS,ASA,AAS etc...(1 vote)
- There are usually little signs used in congruency like (two small lines on a side). So if the triangle congruency is based on it's sides then it is 'side,side,side'(cause a triangle has 3 sides). You can write it as 'side,side,side' or shorten it to SSS. The first congruence and similarity lesson explains further abt this. Check it up if you like!(1 vote)

- How are all equilateral triangles congruent if they vary in side lengths? For example, one equilateral triangle can have side lengths 4 and another can have side lengths 8. That would mean that they are only similar, but not congruent.(1 vote)
- can i git help with this?(1 vote)

## Video transcript

- [Instructor] We're told
in the figure above AB, so the length of that side
right over there is equal to DE, so let me mark that also so AB is equal to DE, and angle A has the
same measure as angle D, so angle A has the same
measure as angle D. Which of the following statements, if true is not sufficient to show that triangles ABC and DEF are congruent? So we have to figure out which
of these is not sufficient, and we only pick one of these, so pause this video and see
if you can figure this out. Okay, so let's go through them one by one, and if any one of these
is sufficient to show that these triangles are congruent then we would rule that out because we wanna figure out which of these choices which is not sufficient to show that the triangles are congruent. Okay, so choice A, AC is equal to DF, so this is saying that AC is equal to DF, so that's saying that we have a side, and then an angle and then another side that is congruent to a side,
angle and another side. Now you might remember from
geometry that side, angle, side which is a way of proving congruence, so this one actually would be sufficient to show that they're congruent, so we would rule it out. This is an interesting
way that they asked this. Alright, this next one BC is equal to EF. BC is equal to EF, so BC is equal to EF right over there. Now is that sufficient for congruence, so this would be angle, side, side which is not a nice abbreviation, so we would say side, side, angle, and you might remember from geometry that this is not sufficient, and one way to think about this is that this angle up here,
the measure of angle B, and the measure of angle
E isn't necessarily fixed, and those aren't necessarily congruent, and so side BC or angle or side EF you could move them out. You can move them out at different angles, and so that would make
DF different lengths, and so side, side, angle is not sufficient to show that the triangles are congruent, so I like this choice a lot, but we could look at the other ones, and see why they are sufficient to show that the triangles are congruent. Angle B has the same measure as angle E, so angle B has the same
measure as angle E. Yep that is angle, side, angle. which is a way to show
congruence and think about this, if this angle and this angle are converted to this angle and that
angle and that side, and between them are the same, well, there's no way that
you could move around the other two sides to get anything other than these triangles being congruent, so we'd rule that out. This is sufficient to show congruence. Angle C has the same measure as angle F. Angle C is the same measure as angle F. Yeah, because here, and I know this is getting confusing now, and actually let me erase some of this other stuff from some
of the previous examples, so now we're saying that the measure of angle C is equal to
the measure of angle F, and think about it this way, if you have two angles that are congruent, that means that the third angle is going to be congruent as well, so you know that they're similar, and then if one set of
corresponding sides are congruent, and they're similar triangles well, then you know you're dealing
with the congruent triangles, or another way to think about it is. This is angle, angle, side which is also a legitimate
way of proving congruence, so this is sufficient, so we rule it out. Triangles ABC and DEF are
equilateral triangles. Well, that also would be
sufficient for showing congruence. Why is that? Because if they're equilateral triangles, then that means all of those
sides have the same length. That side and that side all
to have the same length, and so if all of the sides
of the triangles are the same then you are going to be congruent, so since that is sufficient
to show congruence, we'd rule that out.