Question

8. In the
F
Fig. Q.8
9. ABCD is a parallelogram. CE bisects Cand AF bisects A. In each of the
lour angles A, B, C and D of the parallelogram ABCD
following, if the statement is true, give a reason for the same.
1
(ii) ZFAB =
(i) ZDCE =
2
() ZDCE - ZCEB
(vi) ZCEB= 2FAB
(viii) AE FC
(1) ZA = 20
c.
(iv) ZFAB = ZDCE
(vii) CE | AF
A E
B​

Answer 1

Answer:

2

() ZDCE - ZCEB

(vi) ZCEB= 2FAB

(viii) AE FC

(1

Step-by-step explanation:

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Answer 2

1. ∠A = ∠C ⟹ True; opposite angles in a ||gm are equal.
2. ∠FAB = ½(∠A) ⟹ True; here AF bisects ∠A. Thus, ∠FAB = ∠FAD. So we can say that ∠FAB is the half of ∠A.
3. ∠DCE = ½(∠C) ⟹ True; compare it with 2.
4. ∠FAB = ∠DCE ⟹ True; we can say that ∠A = ∠C because they are the opposite angles in the ||gm. So, half of them will also become same.
5. ∠DCE = ∠CEB ⟹ True; extend DC eastwards. We are given that ABCD is a ||gm, i.e., AB || CD. Since EC will act as a transversal, they become same [alternate interior angles].
6. ∠CEB = ∠FAB ⟹ True; AECF becomes a ||gm because ∠FAB = ∠DCE [prooved]. Now, consider AB as the transversal of AF || CE. ∴ ∠CEB = ∠FAB [corresponding angles].
7. & 8. True; CE || AF and AE || FC because AECF is a || gm and opposite sides of a ||gm are parallel as well as equal.