There is something wrong with this definition for a pair of vertical angles: “If AB and CD intersect at point P,then APC and BPD are a pair of vertical angles.” Sketch a counterexample to show why it is not correct. Can you add a phrase to correct it?
- Umm, for the counterexample, would it be correct if I draw an intersecting line but for APC and BPD I make the angle different?
Smd
To create a counterexample for the given definition of vertical angles, you would need to draw a scenario where two intersecting lines fail to form a pair of vertical angles when connecting specific points.
In this case, you can draw two intersecting lines, AB and CD, that intersect at point P. However, you should then draw angles APC and BPD such that they are not equal or congruent. By doing so, you would have a counterexample that disproves the original statement.
To correct the definition, you can add the phrase "Vertical angles are always congruent" to accurately describe the property of vertical angles. The corrected definition would be: "If AB and CD intersect at point P, then APC and BPD are a pair of vertical angles. Vertical angles are always congruent." This revised definition is more precise and clarifies the property that vertical angles share, which is their equality or congruence.