Question

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

Answer 1

@JakeV8

Answer 2

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

Answer 3

they're top and bottom angles

Answer 4

the ones bisected

Answer 5

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.

Answer 6

true...

Answer 7

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.

Answer 8

yes!(:

Answer 9

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

Answer 10

Thanks (:

Answer 11

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.

Answer 12

This one has me really confuzzled :/

Answer 13

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

Answer 14

look good?

Answer 15

1. Reflexive Property of Equality

Answer 16

@JakeV8

Answer 17

Thanks for helping me :DD

Answer 18

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 :)