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that1chick Group Title

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

  • 2 years ago
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  1. that1chick Group Title
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    @JakeV8

    • 2 years ago
  3. JakeV8 Group Title
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    which angles on the kite are considered the "vertex angles"?

    • 2 years ago
  4. that1chick Group Title
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    they're top and bottom angles

    • 2 years ago
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    the ones bisected

    • 2 years ago
  6. JakeV8 Group Title
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    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.

    • 2 years ago
  7. that1chick Group Title
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    true...

    • 2 years ago
  8. JakeV8 Group Title
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    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.

    • 2 years ago
  9. that1chick Group Title
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    yes!(:

    • 2 years ago
  10. JakeV8 Group Title
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    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

    • 2 years ago
  11. that1chick Group Title
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    Thanks (:

    • 2 years ago
  12. JakeV8 Group Title
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    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.

    • 2 years ago
  13. that1chick Group Title
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    This one has me really confuzzled :/

    • 2 years ago
  14. that1chick Group Title
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    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

    • 2 years ago
  15. that1chick Group Title
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    look good?

    • 2 years ago
  16. that1chick Group Title
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    1. Reflexive Property of Equality

    • 2 years ago
  17. that1chick Group Title
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    @JakeV8

    • 2 years ago
  18. that1chick Group Title
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    Thanks for helping me :DD

    • 2 years ago
  19. JakeV8 Group Title
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    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 :)

    • 2 years ago
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