Question

Proof for parallelogram (fill in the blanks)
Given PQRS is a parallelogram
prove PR and QS bisect each other at T

Answer 1

1) PQRS is a parallelogram
1)

2)PQ is parallel to RS
2)definition for parallelogram

3)m<1=m<3
m<2=m<4
3)

4)PQ=RS
4)opposite sides of a parallelogram are congruent

5)triangle PQT= triangle RST
5)

6)PT-RT
6)

7)
7)definiton of a bisector

Answer 2

Do you know the first answer?

Answer 3

no

Answer 4

The second line says "Given PQRS is a parallelogram"

so reason 1) is simply "given"

Answer 5

as for 3), I would need to see a pic of it to know where angles 1, 2, 3, 4 are

Answer 6

thanks

Answer 7

any ideas why angle 1 = angle 3? and why angle 2 = angle 4?

hint: look at how PQ is parallel to ST

Answer 8

because opposite angles are congruent in a parallelogram

Answer 9

not quite

Answer 10

what kind of angles are 1 and 3?

Answer 11

yeah i cant find that anywhere in my notes

Answer 12

If we have 2 parallel lines

Answer 13

then we cut them with a transversal

Answer 14

then the alternate interior angles



will be congruent

Answer 15

So that's why m<1=m<3 and m<2=m<4

Answer 16

ok so it would just be 3) alternate interior angles

Answer 17

correct

Answer 18

what about for 5 both triangles are congruent which means

Answer 19

how do we know they are congruent?

Answer 20

because in the given column is says triangle PQT= triangle RST

Answer 21

but what is the reason?

Answer 22

how do we justify that?

Answer 23

the triangles have 3 sets of congruent angles and sides

Answer 24

look back at the proof, you'll see that not all 3 sides are used to prove the two triangles are congruent

Answer 25

then just the angles? because we know what the angles are since they are congruent to each other

Answer 26

we have 2 angles, and a side between them, so instead of SSS we use ASA

Answer 27

m<1 = m<3 is one pair of angles
m<2 = m<4 is the other pair

PQ=RS is the set of sides sandwiched between the angles

Answer 28

so 5) would be just ASA

Answer 29

yep ASA property of congruence

Answer 30

and would 6) be SSS because PT and RT are sides as well as QT and ST

Answer 31

no, if you know two triangles are congruent, what can you say about the corresponding pieces?

Answer 32

it's not SSS

Answer 33

what about CPCTC

Answer 34

yep it's CPCTC

Answer 35

and would 7) be PR and QS bisect each other at T

Answer 36

the last statement is ALWAYS the thing you want to prove, so you are correct