Question

Help? There is something wrong with this definition for a pair of vertical angles: "if line AB and line CD intersect at point P, the angle APC and angle BPD are a pair of vertical angles." Sketch a counter example to show y it is not correct.

Answer 1

I don't get this

Answer 2

Tough call. It's not a definition. It's an example.

Answer 3

Is it still possibl

Answer 4

I thought vertical angles are always equal?

Answer 5

They r two angles formed by intersecting lines that share a common vertex, but not a common side

Answer 6

That should help

Answer 7

Draw line AB with A on one side of P and B on the other side of P.
Draw line CD with both C and D on the same side of P.

Answer 8

That's wat I did, I drew a sort of perpendicular lines

Answer 9

Hold on

Answer 10

oh now I get it, :)

Answer 11

I'm confused tk

Answer 12

You probably assumed P was in the middle of A, B, C, and D. Make it otherwise.

Answer 13

Can you draw on this site

Answer 14

I put point p where the two lines intersected

Answer 15

When it says a pair of vertical angles does it mean there r a total of four lines?

Answer 16

That's what I did

Answer 17

But it doesn't prove the statement wrong

Answer 18

O hold on

Answer 19

Perfect. Why do you still doubt? That second one is a counter example. Done! It absolutely proves the statement incorrect. The statement depends on the placement of A, B, C, and D.

Answer 20

my understanding was a little different:

Answer 21

Ok thx tk , sry for this burden

Answer 22

C is coincident with P? Interesting, but Angle APC no longer has any meaning.

What burden? Do you get it, yet, or are you still resisting?

Answer 23

Lol I never thought about putting a and b on the same side of p

Answer 24

I got it

Answer 25

Well, there you go.

Answer 26

R u a teacher?

Answer 27

Tough question to answer. Born and raised, died in the wool, true blue through and through, but no actual credentials or classroom. :-)

Answer 28

I'm in middle school doing this lol