Question

Write a 2-column, paragraph, or flow-chart proof to show that vertex angles of a kite are bisected by the diagonal.

Answer 1

@phi ? @ganeshie8 ?

Answer 2

@amistre64

Answer 3

@ash2326

Answer 4

@waterineyes @Wislar @estudier @eliassaab @eyust707 @edr1c @rebeccaskell94 @Romero @rebecca1233 @richyw @timo86m @thewildones @tunahan @ti22anyxbby @tevawnk @unseenoceans @UMULAS @Ishaan94 @ironictoaster @ivandelgado @itscheli13 @phi @ganeshie8 @guillefix @gitahimart @JahEmpress @julie001 @jagan

Answer 5

can you list the properties of a kite ?

Answer 6

Two disjoint pairs of consecutive sides are congruent by definition

image1.png
Note: Disjoint means that the two pairs are totally separate.

The diagonals are perpendicular.

One diagonal (segment KM, the main diagonal) is the perpendicular bisector of the other diagonal (segment JL, the cross diagonal). (The terms “main diagonal” and “cross diagonal” are made up for this example.)

The main diagonal bisects a pair of opposite angles (angle K and angle M).

The opposite angles at the endpoints of the cross diagonal are congruent (angle J and angle L).

The last three properties are called the half properties of the kite.

Answer 7

The "half property" The main diagonal bisects a pair of opposite angles (angle K and angle M). is what you are trying to prove.

so you probably should only use the first properties:

Answer 8

okay

Answer 9

I would use the very first property
Two disjoint pairs of consecutive sides are congruent by definition
that is a complicated way of saying
sides QP=SP and sides QR=SR

notice you can make 2 triangles QPR and PSR

what can you say about their corresponding sides ?

Answer 10

There the same

Answer 11

you have to be more clear.
what side = what side and why ?

Answer 12

the idea is to show that triangle QPR is congruent to triangle PSR
then you can say that the angle QPR is congruent to angle SPR because they are corresponding parts of congruent triangles

then you say the diagonal RP bisects angle QPS into two equal parts because angle QPR = angle SPR