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Question
primary 6 | Maths
| Geometry
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Date Posted: 5 years ago
Views: 313
QR = TR
△QRT is isosceles.
QR also = SR (both are sides of a square)
So TR = SR
△ SRT is also isosceles
Use the properties of an isosceles triangle to solve
△QRT is isosceles.
QR also = SR (both are sides of a square)
So TR = SR
△ SRT is also isosceles
Use the properties of an isosceles triangle to solve
Thank you very much.
You're welcome
See 1 Answer
According to question, QR = TR. and since PQRS is a square, QR = RS too. Therefore, QR = TR = RS, which makes the angle RTS = angle RST.
The second part of your working is incorrect. The two triangles are isosceles, but they are not neither similar nor congruent.
Angle TRS cannot be 40° as the sum of angle TRS and angle QRT (which gives QRS) would then be 80°, but QRS is actually a right angle (90°), which is a contradiction.
angle TRS = angle QRS - angle QRT
= 90° - 40°
= 50°
Angle RST = (180° - 50°)/2 = 65°
Angle TRS cannot be 40° as the sum of angle TRS and angle QRT (which gives QRS) would then be 80°, but QRS is actually a right angle (90°), which is a contradiction.
angle TRS = angle QRS - angle QRT
= 90° - 40°
= 50°
Angle RST = (180° - 50°)/2 = 65°
Apologies, I labeled 40* at the wrong location causing the mistake. It should be 90* - 40* = 50* then 180* - 50* = 130* divide by 2 = 65*.
Thank you.
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