問二題數學題~~

3. 2x+3x = 180∘(adj. ∠s on st. line)
5x = 180∘
x = 36∘
∠APQ = 2x
= 72∘
∵∠APQ = ∠PQD
∴AB//CD (alt. ∠s eq.)


18. △ABD~△BCD (AAA)
6/10 = 5/x (corr. ∠s, ~△s)
x = 25/3
6/10 = x/y (corr. ∠s, ~△s)
6/10 = (25/3)/y
y = 125/9

1. ∵∠APY +∠BPY=180 °

∴2X +3X =180°
5X=180°
X=36°
∵ ∠XQD=∠CQY=72°
∠APY=2X=2*36°=72°
∴ AB ∥CD

2.∵ ∠BCD=∠ABD,∵ ∠BDC=∠ADB
∴ ⊿BCD ≌⊿ABD
∴AB/BC=AD/BD=BD/CD
6/10=5/X=X/Y
∴X=25/3
Y=125/9

1.
2x + 3x = 180 (adj. angle s on st. lie)
5x = 180
x = 36

angle APQ = 2x
=72
angle XQD = 72
angle XQD = angle APQ
so AB//CD (alt. angle s equal)

2.
Consider triangle ABD and BCD.
angle BCD = angle ABD (given)
angle BDC = angle ADB (given)
angle BCD + angle BDC + angle CBD = angle ABD + angle ADB angle BAD = 180
(angle sum of triangle)
angle CBD = angle BAD
triangle ABD ~ triangle BCD (AAA)
AD/BD = AB/BC (corr. sides, similar triangle)
5/x = 6/10
x = 25/3
AB/BC = BD/CD (corr. sides, similar triangle)
6/10 = x/y
3/5 = (25/3)/y
y = 125/9