# Thread: How to find all angles equal to $$∠BPE$$

1. ## How to find all angles equal to $$∠BPE$$

Find all the angles in Fig 1.2.1 that are equal to ∠BPE
I know that it is equal to ∠DQE is there anything else?
Is there a surefire method to finding out other angles?

2. ## Re: How to find all angles equal to $$∠BPE$$

Originally Posted by littlejon
Find all the angles in Fig 1.2.1 that are equal to ∠BPE
I know that it is equal to ∠DQE is there anything else?
Is there a surefire method to finding out other angles?
First of all, use correct terminology. To say that $\angle BPE=\angle DQE$ means we have one and the same point-set. From the diagram that is false.
What is true: $m(\angle BPE)=m(\angle DQE)$ the measures of those two angles are equal.
Now there are several additional pairs of congruent angles. You tell us what the are.

3. ## Re: How to find all angles equal to $$∠BPE$$

I am going to go with my gut and say that $\displaystyle m(∠BPE) = m(∠DQE) = m(∠APF) = m(∠CQF,)$ are congruent.

4. ## Re: How to find all angles equal to $$∠BPE$$

Originally Posted by littlejon
I am going to go with my gut and say that $\displaystyle m(∠BPE) = m(∠DQE) = m(∠APF) = m(∠CQF,)$ are congruent.
Yes that is correct, good for you.
Now $\displaystyle m(∠APE) = m(∠CQE) ~\&~ m(∠BPF) = m(∠DQE,)$ why?

5. ## Re: How to find all angles equal to $$∠BPE$$

Originally Posted by littlejon
Find all the angles in Fig 1.2.1 that are equal to ∠BPE
I know that it is equal to ∠DQE is there anything else?
Is there a surefire method to finding out other angles?
Are we to assume that line segments AB and CD are parallel? If they aren't then you can't be sure that any angles are equal in measure.

If they are, you need to look up "corresponding angles on parallel lines (the F rule)", "alternate angles on parallel lines (the Z rule)" and "vertically opposite angles (the X rule)".

6. ## Re: How to find all angles equal to $$∠BPE$$

Yes, AB and CD are parallel.

7. ## Re: How to find all angles equal to $$∠BPE$$

Originally Posted by Debsta
Are we to assume that line segments AB and CD are parallel? If they aren't then you can't be sure that any angles are equal in measure.
If they are, you need to look up "corresponding angles on parallel lines (the F rule)", "alternate angles on parallel lines (the Z rule)" and "vertically opposite angles (the X rule)".
@Debsta, I hope that you do realize the there is no universal numbering(labeling, naming) system for axioms, and/or definitions in geometry.

8. ## Re: How to find all angles equal to $$∠BPE$$

Originally Posted by Plato
@Debsta, I hope that you do realize the there is no universal numbering(labeling, naming) system for axioms, and/or definitions in geometry.
Hi Plato,
Yeah I realise that, but if littlejon googles those terms, he'll find what he needs - otherwise he wouldn't know what to look up.
Cheers,
Debsta