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## 8th grade foundations (Eureka Math/EngageNY)

### Course: 8th grade foundations (Eureka Math/EngageNY)>Unit 3

Lesson 3: Topic C: Foundations

# Construct a triangle with constraints

Here's a challenge: in this problem we are given constraints and asked to construct a triangle. It can be done! You'll learn about degenerate triangles, too. Created by Sal Khan.

## Want to join the conversation?

• -Degenerate triangle! I've never heard of this before, but I guess it would have to: two angles of zero, and one of 180; why is is called "degenerate", though?
• A degenerate case is a member of a certain class that is so different from the other members that it belongs to another, usually more simpler class. e.g. a triangle formed by three points all of which are on a straight line is better considered as a line segment. These are the limits of the definition of things. The degenerate triangle satisfies the definition of a triangle (it is a triangle) but it is better/simpler to consider it a line segment.
• I still don't understand what a degenerate triangle is?
• it is the triangle one obtains when one angle has a value of 180 degrees and the other angles are zero.
• In mathematical terms, a constraint is a predefined condition that has to be met. It is called a constraint because it constrains, i.e. limits or restrains, the many ways you could tackle something. It applies to everything, not just triangles. In the video, Sal shows how to draw a triangle - however, not just any triangle, but a triangle that has to meet certain requirements (constraints), for example, it has to have the side lengths 3, 3, and 5. These are constraints that the triangle has to meet.

There might be constraints that make it impossible to build the triangle (such as side lengths 2,2, and 5) or constraints that only yield one unique way of building the triangle (see the last triangle with side lengths 3,3, and 5). A constraint could also be to draw a triangle that has a right angle.
• All of the sides of a triangle has to = 180 degrees
• Who walk up to you and ask you that?
• Maybe a math teacher?
• What is a line segment?
• A line segment is a geometric figure that consists of two distinct points, called endpoints, and all the points straight between the two endpoints.

Note that a line segment has finite length, though it contains infinitely many points.
• This is not what I'm looking for, this is the question I cannot figure out:

Q1. Construct a right-angled triangle containing an angle A such that sin A = 0.4.

Help me?
• I have no clue what i just watched
• i can tell that the triangle at could never really work but it still doesn't really make cense can someone help a sister out
• they have to be able to reach, that's all
it's not a triangle yet if one of the corners is left standing open or if one of the lines sticks out on it's own?
so the sides have to be long enough so any two of the sides added together equals longer than the leftover side
just like all the angles in a triangle have to add up to 180 degrees so the corners can meet
otherwise the three lines can't close to make the triangle
it's so simple it's gorgeous
this is something you will always be able to rely upon about triangles, and why triangles are used for measuring and navigation and why there's such a thing as trigonometry which is...
nm
the ends have to reach
:)