1. In figure, DE // AC and DF // AE. Prove that BF/FE = BE/EC.(2)
2. In the, DE || BC. Find the length of side AD, given AE = 1.8 cm,BD
= 7.2 cm and CE = 5.4 cm. (2)
3. In figure, XY || QR, PQ/XQ=7/3 and PR = 6.3 cm, find YR. (2)
4. D and E are points on sides AB and AC of triangle ABC such that
DE || BC. If AD = 2·4 cm, DB = 3.6 cm and AC = 5 cm, find AE. (3)
X and Y are points on the sides AB and AC respectively of a triangle
ABC such that AX/AB= ¼, AY = 2 cm and YC = 6 cm. Find whether
XY || BC or not. (3)
5. If a line segment intersects sides AB and AC of a ∆ABC at D
and E respectively and is parallel to BC, prove that AD/AB=
AE/AC. (3)
6. In the given figure, altitudes AD and CE of ∆ ABC intersect each
other at the point P. Show that:(i) ∆AEP ~ ∆ CDP (ii) ∆ABD ~ ∆
CBE (iii) ∆AEP ~ ∆ADB (iv) ∆ PDC ~ ∆ BEC (5)
7. In given figure, EB ⊥ AC, BG ⊥ AE and CF ⊥ AE. (5 Marks)
Prove that: (a) ∆ABG ~ ∆DCB (b) BC/BD= BE/BA. (5)
2. In the, DE || BC. Find the length of side AD, given AE = 1.8 cm,BD
= 7.2 cm and CE = 5.4 cm. (2)
3. In figure, XY || QR, PQ/XQ=7/3 and PR = 6.3 cm, find YR. (2)
4. D and E are points on sides AB and AC of triangle ABC such that
DE || BC. If AD = 2·4 cm, DB = 3.6 cm and AC = 5 cm, find AE. (3)
X and Y are points on the sides AB and AC respectively of a triangle
ABC such that AX/AB= ¼, AY = 2 cm and YC = 6 cm. Find whether
XY || BC or not. (3)
5. If a line segment intersects sides AB and AC of a ∆ABC at D
and E respectively and is parallel to BC, prove that AD/AB=
AE/AC. (3)
6. In the given figure, altitudes AD and CE of ∆ ABC intersect each
other at the point P. Show that:(i) ∆AEP ~ ∆ CDP (ii) ∆ABD ~ ∆
CBE (iii) ∆AEP ~ ∆ADB (iv) ∆ PDC ~ ∆ BEC (5)
7. In given figure, EB ⊥ AC, BG ⊥ AE and CF ⊥ AE. (5 Marks)
Prove that: (a) ∆ABG ~ ∆DCB (b) BC/BD= BE/BA. (5)
