math problems

2007-12-02 10:15 am

1. In the figure,ABCD is a square and ABE is an equilateral triangle.∠ADE = ?
A. 72°. B. 74°
C. 75° D. 76°
Figure http://aycu21.webshots.com/image/34300/2006350544508177680_rs.jpg

2. In the figure, AB = BC = CD. Find∠AED.
Figure http://aycu11.webshots.com/image/36250/2006375821563852068_rs.jpg

3.In the figure, AD : DB = 1 : 2 , AE : EC = 3 : 2. Area of △BDE : area of △ABC=
A. 1:3
B. 2:5
C. 3:4
D. 4:25

更新1:

3 Figure http://aycu11.webshots.com/image/36250/2006365178752493313_rs.jpg

回答 (1)

魏王將張遼

2007-12-02 5:31 pm

✔ 最佳答案

(1) Since △ABE is an equilateral triangle, we have:
∠ABE = ∠AEB = ∠BAE = 60°
Also, since AE = AD, △ADE is an isoceles triangle and therefore,
∠DAE = 30°
∠ADE = ∠AED = (180° - 30°)/2 = 75°

(2) Join CE and BE, we have:
△ABC is an isosceles triangle with ∠ACB = 25°
Then ∠AEB = ∠ACB = 25° (Angles in the same segment)
∠CEB = ∠DEC = ∠AEB = 25° (Equal chords, equal angles)
∠AEE = ∠CEB + ∠DEC + ∠AEB = 75°

(3) Comparing △ABC and △ABE, they have the same height and their base ration is AE : AC = 3 : 5
Therefore their area ratio = 3 : 5
So △ABE area is 3/5 of △ABC
Comparing △BDE and △ABE, they have the same height and their base ration is BD : BA = 2 : 3
Therefore their area ratio = 2 : 3
So △BDE area is 2/3 of △ABE
Finally, △BDE area is 2/5 of △ABC

參考: My Maths knowledge

👍 0 👎 0