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Course: Geometry (FL B.E.S.T.)>Unit 5

Lesson 2: Working with triangles

Finding angles in isosceles triangles

The measures of two angles of an isosceles triangle are 3x+5 and x+16. Find all possible values of x. Created by Sal Khan.

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• What is an isosceles triangle?
• An isosceles triangle is a triangle which has at least to sides equal to each other. Notice that all equilateral triangles are isosceles.
• can we write an angle in decimal form? like measure of angle ABC = 95.55
• Yes you can, but they are usually written in degrees-minutes-seconds.
so 95.55 = 95º 33' (ninty five degrees, thirty three minutes).
or 95.44444 = 95º 26' 39.98" (Here, after seconds we write decimals...)
However, I only do this because my calculator has a key for doing it easely, on other situations using decimals should be perfectly fine.
• can u do questions that ask find the x of an iscoseles triangle and with a given angle?
• The sum of angles in a triangle are 180, and if you have an iscoseles triangle, the angles opposite the congruent sides are congruent also. So if you have x as one of the angles opposite and a vertex angle of x + 30, the other opposite angle is also x, so x + x + x+ 30 = 180 which you can solve.
• how do you know if you use the number twice in the equation or the x??
• In an isosceles triangle, there are two base angles and one other angle. The two base angles are equal to each other. So say you have an isosceles triangle, where only two sides of that triangle are equal to each other. And then you have 36 degrees as one of your base angles. The other base angle will equal 36 degrees too.

36 + 36 + x = 180 degrees

36 + 36 = 72
72 + x = 180
180 - 72 = 108
x = 108.

REMEMBER: THIS ONLY WORKS IF YOU HAVE TWO BASE ANGLES. IN THIS CASE, WE HAD TO USE THE NUMBER TWICE (BECAUSE OF THE BASE ANGLES) AND X (DENOTE THE UNKNOWN NUMBER). I REALIZE YOU PROBABLY ALREADY FOUND HELP ANSWERING YOUR QUESTION; BUT IF NOT, HERE IT IS.
• Is there a video explaining the hinge theorem? I need to see it.
• What does congruent mean?
• Two shapes are congruent if they have the same shape and size. Or, any shape that can be translated, rotated, or reflected to match another shape means that those two shapes are congruent.
• Can a triangle have negitive angles or is that impossible?
• In geometry, all angles measurements are positive, at least in the geometry we are studying on this site.
In Trigonometry (after you finish with the simplest levels--trigonometry of right triangles) and also in Calculus and Physics and when studying vectors, and in other similar maths, angles are just as likely to be positive as negative because `positive angles rotate counterclockwise` and `negative angles rotate clockwise`.
Even more mind-blowing is that lengths can be positive or negative depending on their direction and location relative to the starting point. This allows us to describe the motion of rockets and speeding atomic particles and many other interesting things.
• What is congruent and what is it used for?
• You can set up numbers or variables as equal such as 6=6 or x=6 or 3x+2=8. Congruent is used for figures which have the same shape and size. If you are building, you often want a bunch of boards that are all congruent. Machines make parts that are all congruent so that you can replace them. In math, if two figures are congruent, we can solve for parts of the figure because we know that congruent sides/angles have equal measures.