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# CA Geometry: Triangles and parallelograms

21-25, triangles and parallelograms. Created by Sal Khan.

## Want to join the conversation?

• I'm al little confused on Problem 23.
• Here is a little hint. Remember alternate interior angle theorem. I was confused for quite a while on this kind of stuff, but once I got the hang of it, it was easy. Don't worry, you'll get it.
(1 vote)
• For #22, don't u have to follow pythagreom thereom?
• You can use pythagorean theorem to solve the problem if that is the method that you are most comfortable with, but the way Sal is showing, in which the sum of two of the sides must be greater than the length of the other side in order for the lengths to form a triangle, works just as well. In fact, I think Sal's method is the lesser time-consuming method between the two.
• I am confused on problem 21 can anyone clear it up for me
• There is this thing called the 'triangle inequality' which says, 'given two sides of a triangle a and b (a>=b), the third side x can be no smaller than (a-b) and no larger than (a+b). [ officially stated as (a-b) < x < (a+b) ]

Imagine a triangle has legs that are whole number lengths, one is 4 and the other 7. If the third side were 3 then it wouldn't be a triangle because it would have no middle... same problem if the third side were 11. And if the third side were 12 the 7 length side and the 4 length side wouldn't be able to touch, so the figure wouldn't be closed.

So in this problem, two legs are a and the third is 15, so (a - a) < 15 < (a + a). a - a is zero so that side doesn't matter but the other side is 15 < a + a or 15 < 2a or 7.5 < a. since a is known to be a whole number it must be 8 or greater. There is only one answer 8 or greater, so that is the right one.
(1 vote)
• For what value of x is the given parallelogram a rhombus represented by (6x+9) and (9x-9)?
• The sides of a rhombus are all congruent, so 6x+9=9x-9. Then, 3x-9=9. Then, 3x=18, and finally x=6
(1 vote)
• At , Sal challenges us to draw a parallelogram where parallel sides aren't equal. Then, he says that you can't. But doesn't an isosceles trapezoid fit this requirement?
Help!
(1 vote)
• I'm having trouble with a question and its "in triangle PQR. Angle P is congruent to Angle R and the measure of Angle Q is twice the measure of Angle R. Fine the measure of each angle."
(1 vote)
• Triangles have measures that add up to 180 degrees. Because of so, the following system of equations can be modeled:

P+R+Q=180

Now we need to substitute everything relative to R, simply because using R is easier (You can use others if you want).

R+R+2R=180

Since P=R
R=R
and Q=2R

so simplify that and you get
4R=180
R=180/4

You can plug that into a calculator or solve it yourself for the decimal, or you can simplify the fraction, depending on what they ask for.

Hope this helps! Let me know if you have more questions. :D