00:01
Here we're given three vertices of a parallelogram.
00:04
Q, which is the point 85, so that's here.
00:10
R, which is 5, 1, so that's that point right there.
00:15
And s, which is the point 25.
00:20
And then we have to prove that this parallelogram pqrs is a rhombus.
00:26
So i'll show pqrs is a rhombus.
00:36
Well that means it has to satisfy certain conditions, and we're going to prove that all those conditions hold.
00:45
They start us off with the statement 1, sr is equal to 5, reason being pythagorean theorem.
01:02
And if you were to draw an xy -plane in here, it would be easy to see the theorem.
01:09
Because if you make a, let's see, sr is this line segment here.
01:17
If you were to draw a line straight down towards the x -axis to get a 90 degree angle, then this length here, or this would be the point, x is 2, y would be 1, because it's at the same height as r.
01:37
So this length here then, between this point and s, would be 5 minus 1 is 4.
01:45
The distance between that point and r is the difference in x values, which is 5 minus 2, so that is 3.
01:53
And by the pythagorean theorem, the length between s and r would be the square root of 4 squared plus 3 squared, which is the square root of 25, and that is 5.
02:06
So that's where that first statement comes from.
02:09
Then the second statement we have to fill out.
02:13
When we know that sr is equal to 5, then by that same reasoning, if we were to draw a right angle here, then this length is 4, this length is 3, so this length has to be 5.
02:32
So we can say that qr equals 5, because of the pythagorean theorem.
02:43
Pythagorean theorem.
02:46
So this is your answer for a, this is a, and this is your answer for b.
02:59
And then going on to the next line statement, they tell us that sr is equal to qr.
03:08
Well, that's true, because they're both 5, so that's the substitution property of equality.
03:13
They're both equal to 5, so we can substitute.
03:16
4 says sr is congruent to qr.
03:22
Sr, this piece right here, is congruent to qr, this one right here, because they're equal in length, and that's the definition of a congruent line segment, that they're equal in length.
03:38
So sr is congruent to qr, because they're equal in length, and that's the definition of congruent line segments.
03:49
Then in 5, they say ps is congruent to qr.
03:57
Well, where is ps? this is ps, and it's congruent to qr because they are parallel to each other, and they're parallel to each other because they're opposite sides of a parallelogram, and they have endpoints at equal distance there...