Question

Prove that the diagonals of the square bisect the interior angles.

Answer 1

@jim_thompson5910

Answer 2

to prove that a bisection occurs, you need to show that the two smaller pieces (after the bisection) are equal and congruent

Answer 3

so do i do like a chart like showing reason and stuff like that

Answer 4

yes

Answer 5

that's one way to do it

Answer 6

ok but i dont know what to do really

Answer 7

do you know how to prove that triangle PSQ is congruent to triangle RSQ

Answer 8

no not really

Answer 9

ok one second

Answer 10

first off, you agree that all sides of a square are congruent right?

Answer 11

yes

Answer 12

so you can use this, along with the shared common diagonal to prove that the inner triangles are congruent

Answer 13

Given: square PQRS with diagonals PR and SQ PT is congruent to RT and ST is congruent to TQ Right angles STP, STR, RTQ, PTQ Prove: PR bisects angles SPQ and SRQ SQ bisects angles PSR and PQR 1. PQRS is a square 1. Given 2. PQ is congruent to QR is congruent to RS 2. Def of square is congruent to SP 3. Angles STP, STR, RTQ, PTQ are right angles 3. Given 4. Triangles STP, STR, RTQ, PTQ are right triangles 4. Def of right triangle 5. ST is congruent to QT 5. Given 6. Triangle STR is congruent to triangle QTR 6. HL 7. Angle SRT is congruent to angle QRT 7. CPCTC 8. PR bisects angle SRQ 8. Def of angle bisector Similarly PR bisects angle QPS and SQ bisects angles PSR and PQR

Answer 14

is that right

Answer 15

hmm it's kinda a jumbled mess

is it supposed to look like that?

Answer 16

well no thats why i tagged you on that page that i found it

Answer 17

oh ok, let me check my messages then