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### Course: Integrated math 1>Unit 17

Lesson 5: Working with triangles

# Isosceles & equilateral triangles problems

Isosceles triangles have two congruent sides and two congruent base angles. Equilateral triangles have all side lengths equal and all angle measures equal. We use these properties to find missing angles in composite figures. The problems are partly from Art of Problem Solving, by Richard Rusczyk. Created by Sal Khan.

## Want to join the conversation?

• What are conjugate angles?
• Conjugate angles are a pair of angles that add up to 360 degrees. E.g. 60 degrees and 300 degrees.
• How to prove a 30, 60, 90 degrees angle triangle's hypotenuse is always two times the side that opposite the 30° angle?
• Nice question!

Draw a 30-60-90 triangle and its reflection about the leg opposite the 60° angle. These two 30-60-90 triangles together form a larger triangle. This larger triangle has three 60° angles and is therefore equilateral!

The hypotenuse of either one of the 30-60-90 triangles is one of the sides of the equilateral triangle. The sides opposite the 30° angles of the two 30-60-90 triangles are equal in length, and the two of them together form another side of the equilateral triangle.

It then follows that the length of the side opposite the 30° angle of a 30-60-90 triangle is half the length of the hypotenuse!

Have a blessed, wonderful day!
• How can you remember the difference between equilateral and isosceles triangles?
• Hmmm....well, equilateral is equal all around that easy.
Isosceles is a bit harder; you could remember that there is one isolated side that’s not like the other two. Since isolated sounds like isosceles a little.
That’s all I can think of right now.
Merry Christmas and Jesus loves you❤️
• huh? I still do not understand this😅
• What part? Finding the angles in general? Finding supplementary? Well, I don't know which one you need help with, but here is some tips:
"Straight" for Supplementary (Because it is straight, 180 degrees)
"Corner" for Complementary (Because it makes a corner, 90 degrees)
All of a triangle's angles add up to 180 degrees, but not squares, though! Square's angles add up to 360 degrees, if that make since? Half of a square is a triangle, so that is correct. :3

If you need more help, feel free to ask for help!
-Duskpin, the avatar
• I know complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees but is there a word for angles that add up to 360 degrees?
• wow its been 10 years since you posted this thats when i was 4 years old
• How do you remember the difference between supplementary and complimentary angles?
• I hate to break it to you, but you're just going to have to memorize it. But fear not, after practicing for about a week, I'm sure you'll know it!
Good luck!
• "At ,Why segment AB and BC equal to segment CD?" It seems segment CD is a lot wider than AB and BC.
• You are correct in that drawings are not always to scale, but if it is stated that they are equal, we rely on what is stated, not what appears to be true.
• Why does a triangle add up to 180 ?
• Because that's the only solution for triangles. The sum of the angles will always be 180 degrees.
• At , Sal says that all equal sides of a triangle are 60 degrees. Does this apply to any type of triangle as long as they have the same congruent sides?
• Only equilateral triangles have angles that are all equal to 60 degrees.
• If the expressions are the equal legs of an isosceles, or equilateral triangle, then we should go

• Create an equation with the equivalent expressions, by setting them equal to each other,

then solve for x using algebraic methods, (by keeping the equation balanced by performing the same math operations on both sides), to…

• Isolate x to one side of the equation am I right?