13. In a square ABCD, the bisector of the angle BAC
cuts BD at X and BC at Y. Prove that the triangles
ACY, ABX are similar.
(SC)
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Answer:
If in a Square ABCD
bisector of <BAC cut BD at X & BC at Y then AACY
= AABX
Step-by-step explanation:
in a square Diagonal are angle bisectors
=> <BAC = 2ACB = 90 ° / 2 = 45 °
also ZABD = 45°
Lets compare A ACY & AABX
A ACY
2 CAY = (1/2) 2 BAC = (1/2) 45° = 22.5°
ZACY ZACB = 45° (as Y lies on BC)
ZCYA = 180 ° -45 ° -22.5 ° = 112.5 °
AABX
ZXAB=(1/2)<BAC = 22.5° ZABX = ZABD = 45° (as X lies on BD) ZAXB = 180°-45°-22.5° = 112.5°
now
2 CAY = 2XAB = 22.5°
ZACY ZABX
= 45°
ZCYA = ZAXB = 112.5 ° => AACY = AABX
AACY & AABX are similar.
Step-by-step explanation:
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