## that1chick 3 years ago Tell me if this is right!? (: Write a 2-column, paragraph, or flow-chart proof to show that vertex angles of a kite are bisected by the diagonal. Statement: Reason: 1. triangle PSR is congruent to PQR 1. SSS congruency 2. ∠QPS = ∠QPR + ∠SPR and ∠QRS = ∠QRP + ∠SRP 2. Definition of a Kite 3. the corresponding angles are congruent 3. CPCTC

1. that1chick

2. that1chick

@JakeV8

3. JakeV8

which angles on the kite are considered the "vertex angles"?

4. that1chick

they're top and bottom angles

5. that1chick

the ones bisected

6. JakeV8

The top and bottom angles can't be congruent with each other... the top is practically always "fatter" than the bottom of a kite. If they were congruent, it would look more like a straight diamond.

7. that1chick

true...

8. JakeV8

But that's not what you need to prove... You just need to prove that the vertex angles (which probably aren't congruent) are both bisected by the kite diagonal.

9. that1chick

yes!(:

10. JakeV8

I can't remember "SSS congruency".... that might be ok. I would have started with a statement that PR = PR by "Reflexive" I think you can probably state that the angles at Q and S are congruent by the definition of a kite... (I don't know, I didn't take Kite Geometry) Then maybe you can use side PR and the congruent angles Q and S to show that the two side triangles are congruent. If they are congruent, then corresponding angles of congruent triangles are congruent. The small half-angles that are the result of the diagonal bisector PR are corresponding to each other... and since the triangles are congruent, those angles are congruent. Last step, state the angles are bisected because the two partial angles are congruent, by reason of "definition of a bisector" or something like that. I'm sorry I don't know it exactly... it's been awhile since I did geom proofs

11. that1chick

Thanks (:

12. JakeV8

hope it helped... it was a bit rambly, but maybe the reasoning can remind you of the "official" names of the reasons you are supposed to use. I am good at seeing that it is true, but less good at providing the "approved geometry reasons" for the proof.

13. that1chick

This one has me really confuzzled :/

14. that1chick

Statement: Reason: 1. PR = PR 1. Reflexive 2. ∠Q = ∠S 2. Definition of Kite 3. PS = PQ 3. Definition of Kite 4. triangle PSR is congruent 4. CPCTC to triangle PQR 5. ∠QPR = ∠SPR and ∠QRP = ∠SRP 5. Definition of Congruent Triangles 6. PR bisects ∠QPS and ∠QRS 6. Definition of a Bisector

15. that1chick

look good?

16. that1chick

1. Reflexive Property of Equality

17. that1chick

@JakeV8

18. that1chick

Thanks for helping me :DD

19. JakeV8

I think reason 5 should be CPCTC... you are saying the two angles are congruent BECAUSE they are corresponding parts of congruent triangles. Also, I think reason 4 might need to be something like SSA... "side side angle" but I can't remember that for sure... Otherwise, it looks good... good persistence :)