聚源中学8年级数学6

2020年11月25日发(作者：童大林)
square ABCD, M is the midpoint of AD and N is the
midpoint of MD. Prove that ∠NBC = 2∠ABM.




2.(CHINA/1995) In △ABC, ∠A = 90
°
;AB = AC, D is a
point on BC. Prove that BD
2

+ CD
2

= 2AD
2
.










that Rt△ABC has a perimeter of 30 cm and an area
of 30 cm
2
. Find the lengths of its three sides.











4. In the Rt△ABC, ∠C = 90
°
, AD is the angle bisector of∠
A which intersects BC at D. Given AB = 15 cm, AC = 9 cm,
Find the distance of D from AB.









the right triangle ABC, ∠C = 90
°
，BC = 12 cm, AC = 6
cm, the perpendicular bisector of AB intersects AB and BC at
D and E respectively. Find CE.








6. In the rectangle ABCD, CE ⊥ DB at E, BE =
1
4
BD and
CE = 5 cm. Find the length of AC.










7: In △ABC, ∠C = 90
°
, D is the mid-point of AC. Prove
that AB
2
+ 3BC
2

= 4BD
2
:











8: In the right triangle ABC, ∠C = 90°， E、D are points on
AC and BC respectively. Prove that AD
2

+ BE
2
= AB
2

+ DE
2
: