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### Course: 8th grade (Eureka Math/EngageNY) > Unit 2

Lesson 3: Topic C: Congruence and angle relationships- Congruence and similarity — Basic example
- Congruence and similarity — Harder example
- Angles, parallel lines, & transversals
- Parallel & perpendicular lines
- Missing angles with a transversal
- Angle relationships with parallel lines
- Measures of angles formed by a transversal
- Equation practice with angles
- Angles in a triangle sum to 180° proof
- Triangle exterior angle example
- Find angles in triangles
- Find angles in isosceles triangles
- Worked example: Triangle angles (intersecting lines)
- Worked example: Triangle angles (diagram)
- Finding angle measures between intersecting lines
- Finding angle measures using triangles
- Triangle angle challenge problem
- Triangle angle challenge problem 2

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# Congruence and similarity — Harder example

Watch Sal work through a harder Congruence and similarity problem.

## Want to join the conversation?

- Sal puts easy videos in harder cases....lol(44 votes)
- Great now how do I do it in a minute :/(12 votes)
- by doing it in 20 seconds(23 votes)

- how is this the harder example(17 votes)
- These type of question are normally easy for people.(7 votes)

- how do we know if the two lines are parallel?(2 votes)
- to make it simpler, in the school hall you and your friend walk beside each other to go to class, you are parallel/ next to each other without ever becoming each other or being in the exact same place at the same time(15 votes)

- What percentage of SAT math questions are like this?(7 votes)
- Not a very big percentage, its about 10-12 percent i guess(9 votes)

- How would we know that 40 + 40 could have been replaced with anything else. Because it never says x and x for the problem, but instead leaves it blank.

So instead of 40 and 40, it could have been 50 and 30, or 60 and 20. This would have changed the problem greatly.(0 votes)- This is because triangle ABC is isosceles. You can draw a line dividing every isosceles triangle by bisecting the angle in between the sides of equal length. This leaves you with two new triangles, who are congruent to each other by SAS. Then you can conclude that all corresponding angles will be congruent. One pair of corresponding angles in these triangles are the actual other two angles of the isosceles triangle. These have to be equal, in every isosceles triangle.

It's pretty handy to just keep this statement in mind for the SAT: When you have an isosceles triangle, not only the two sides, but also the two angles that aren't in between the congruent sides are congruent.(12 votes)

- why can't we use the transversal angel theory to find p(2 votes)
- Because we are not given any parallel lines in this exercise.(7 votes)

- why does it equal 180?(3 votes)
- The interior angles in any closed triangle add up to 180 degrees(4 votes)

- How did we know that Angle P was a "vertical angle" with that other angle below it?(3 votes)
- How do we know when 2 lines are not parallel(2 votes)

## Video transcript

- [Instructor] In the figure above, triangle ABC is isosceles. So that's triangle ABC. So that big triangle, that's isosceles, which means two of its
sides are congruent, have the same length. That is side AB, they explain it here, side AB, so side AB here is equal in length to side BC. So these two sides are
equal, equal in length. So we could say that that
side is equal to that side. Actually, I wanna be careful, just because that looks like I'm saying that from that point to that point, but those two blue sides are
gonna be equal in length. Triangle DEF, DEF, overlaps with triangle ABC. Yeah, we see that, they kinda
form this Star of David, or kinda this skewed Star of David. What is the value of angle p here? All right, let's work through this. So ABC is an isosceles triangle, and I'm gonna draw it separately here. So ABC is an isosceles triangle. This is an isosceles triangle. And an isosceles triangle if these two, if these two sides are congruent, then these base angles
are going to be congruent. And they already tell us
that this angle up here, they already tell us that this
angle up here is 100 degrees, and we know that all the interior angles of a triangle add up to 180 degrees. So if we call, if we call this x degrees, and then this is x degrees, then we see that x plus x plus 100, plus 100, is going to
need to be equal to 180. Or we can get that two x, two x, and then if we subtract
100 from both sides, is equal to 80, or that
x is equal to 40 degrees. So just like that,
we're able to figure out that both of these, both of these are going to be equal to 40 degrees. And that came straight out of the fact that ABC is an isosceles triangle. These two base angles are
going to be congruent. So this is 40 degrees
and this is 40 degrees. Now, now let's go to this
little small triangle right over here, this little
small triangle right over here. Once again, we know
that the interior angles of a triangle add up to 180 degrees. So if this right over here, actually this angle right over here is going to be the same as
p, because it's vertical. It's a vertical angle with p. So this is going to be p degrees as well. And now, we see p plus 40, p plus 40 plus 60, plus 60, is going to
add up to 180 degrees. That's the interior angles
of this little small triangle right over here. Or, we could write p plus, if we add the 40 and the 60, you get 100, p plus 100 is equal to 180. If we subtract 100 from both sides, we get p is equal to 80 degrees. So what is the value of p,
or I guess this is p degrees? So the value of p is,
the value of p is 80.