Question

A person is making a paper airplane from a square sheet of paper.

Beginning with a perfectly square piece of paper, fold 1 is made such that point Q lands on point S. the paper is then unfolded, leaving a crease from P to R.

(I will draw the diagram in the comments)

for folds 2 and 3, edges PQ and PS are folded onto PR.
1. is point T between points Q and R?

2. is point T midpoint of segment QR.

3. which angle is bisected by fold 2?

4. remember that the sheet of paper starts out as a square. Find the following angle measurements in degrees:

a) 12 years ago

Answer 1

1. If edge PQ is folded to fall on PR, it will form the crease PT in between PQ and PR and therefore point T has to fall in between points Q and R.

Answer 2

2. No, T will not be the midpoint of QR. By making edge PQ fall on PR, the crease PT bisects the angle QPR. Since sides PQ and PR are of different lengths, QT and TR will be of different lengths and so T will not be the midpoint of QR.

Answer 3

3. Fold 2 bisects angle QPR.

Answer 4

4. PQRS is a square. So what is angle QPS?

Answer 5

Each of the four angles within a square is 90 degrees. Since PQRS is a square, angle QPS happens to be one of the four interior angles of a square and therefore angle QPS is 90 degrees.

b) What is angle QPR?
Note: Angle QPS is 90 degrees and PR is the diagonal to the square. The diagonal bisects the angle QPS. Therefore, angle QPR = ?

Answer 6

If angle QPS is 90 degrees and the line PR bisects the angle, how much will each angle be?
Bisects means divides the angle into two equal parts.

Answer 7

correct. angle QPR = 45 degrees.

c) PT bisects angle QPR. So what will angle QPT be?
Remember, bisects means divides the angle into two equal parts.

Answer 8

correct.
In fact, angle QPT = angle TPR = angle RPU = angle UPS = 22.5 degrees ---- (1)

d) angle TPU = ?
angle TPU = angle TPR + angle RPU = ? (look at equation (1) )

Answer 9

angle QPT = 22.5 degrees
angle TPR = 22.5 degrees
angle RPU = 22.5 degrees
angle UPS = 22.5 degrees

d) angle TPU = angle TPR + angle RPU = ?

Answer 10

correct. d) angle TPU = 45 degrees.

e) angle QPU = ?
angle QPU = angle QPR + angle RPU
we already found angle QPR in b)
and angle RPU is mentioned in my previous reply. Add them up to find angle QPU.

Answer 11

Yes. e) angle QPU = 67.5 degrees.

f) angle PTR = ?

Three angles of a triangle add up to 180 degrees.
In triangle PTR, angle PTR + angle TPR + angle PRT = 180 degrees.
Therefore, angle PTR = 180 - angle TPR - angle PRT ------ (2)
angle TPR is mentioned in 2 replies ago.
angle PRT = 45 degrees because the diagonal PR bisects the 90 degree angle of a square.
plug the numbers into (2) and find angle PTR.

Answer 12

f) angle PTR = 180 - angle TPR - angle PRT
= 180 - 22.5 - 45
= 112.5 degrees

g) angle PTQ = ?
angle PTQ + angle PTR = 180 degrees
angle PTQ = 180 - angle PTR
angle PTR = 112.5 degrees (from f) )
so angle PTQ = 180 - 112.5 = 67.5 degrees.

Answer 13

so a) = 90 b) = 45 c)= 22.5 d)= 45 e)=67.5 f)=112.5 g)=67.5 @ranga

Answer 14

and thank you so much for helping!! @ranga

Answer 15

Yes, a) through g) looks correct.

You are welcome.