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please answer Q 20.

please answer Q 20. • JCBA.J
E is the mid-point
17. In the given figure. ABCD is a parallelogram,
or BC. DE produced meets AB produced at L
Prove that ;
AL — 2 DC.
18. Equilateral triangles ABD and ACE are drawn on the sides AB
and AC of A-ABC as shown in the figure. prove that .
DC BE.
(i) zmc LEAB
(Hint. (i) + ZBAC and LEAB 600 + MAC.
Join DC and BE and show that ADAC ABAE.]
19. In the given figure, ABCD is a square and P, Q, R are points
On -4B, BC and CD Such that AP BQ CR and
.ZPQR - 90'.
Prove that :
(iii) ZQPR - 450
[Hint. AB PB = QC
Ext ZRQB ZQC'R ZQRC = 900 + ARC.
Also, ,ZRQB = 900 + ZPQB.
ZQRC = ZPQB
Note, show that APBQ AQCR.J
20. In the given figure, ABCD is a square, EF II BD and R is the
(ii) AR bisects ZBAD
(iii) If AR is p
, it will pass through C.
21. ABCD is a parallelogram in which and ZC are obtuse.
Points X and Yare taken on diagonal BD such that LAXD
zCYB 900. Prove that : XA = YC.
98
ConstrucUon : From W.
Statement
i. and
zxnc
Hence,
Theorem 2. (Converse o'
c
Foundation Mathematics for Class IX
to them are
TO prove XB XC.
Construction From år
Proof.
State
2. xXCO
Henee,
Triangles