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Standard VIII

Mathematics

Properties of Angles Formed by Two Parallel Lines and a Transversal

In the figure...

Question

In the figure given, $B D ∥ A E$ . If $¯ ¯¯¯¯¯¯ ¯ C E = 3$ cm, what is the length of $¯ ¯¯¯¯¯¯ ¯ A C$ ?

4

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3 \sqrt{3}

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3

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5

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Solution

The correct option is D $3$
Given $B D | | A E C E = 3 c m$
Since $B D | | A E$ and $A C$ is transversal
$∠ C A E = x$
Similarly $B D | | A E$ and $C E$ is transversal
$∠ C E A = x$
In $△ A C E$
$∠ C A E = ∠ C A E = x$
$⟹ A C = C E$
$⟹ A C = 3 c m$

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Similar questions

Q. In the given figure,

A E ∥ D B, B C = 7 c m, B D = 5 c m, D C = 4 c m

. If

C E = 12 c m,

find

A E

and

A C

Q. In the given figure,

A D = 3 c m, A E = 5 c m, B D = 4 c m, C E = 4 c m, C F = 2 c m, B F = 2.5 c m

, then find the pair of parallel lines and hence their lengths.

Q. In the figure shown

D E ∥ B C

and

A D = 3 x - 2, A E = 5 x - 4, B D = 7 x - 5

and

C E = 5 x - 3

. Therefore, the value of

x

In a \Delta ABC, D and E are points on the sides AB and AC respectively such that DE||BC.
(i) If AD = 6cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If $\frac{A D}{D B} = \frac{3}{4}$ and AC = 15 cm, find AE.
(iii) If $\frac{A D}{D B} = \frac{2}{3}$ and AC = 18 cm, find AE.
(iv) If AD = 4, AE=8, DB =x-4, and EC = 3x - 19 find x
(v) If AD = 8 cm, AB=12 cm and AE = 12 cm, finde CE.
(vi) If ad = 4 CM, db = 4.5 cm and AE = 8 cm, find AC
(vii) If AD = 2 cm, AB = 6 cm and AC = 9cm, find AE.
(viii) If $\frac{A D}{B D} = \frac{4}{5}$ and 3C = 2.5 cm, find AE.
(ix) If AC=x, DB=x-2, AE=x+2 and EC=x-1, find the value of x.
(x) If AD= 8x -7. DB= 5x-3, AE=4x-3 and EC= (3x-1), find the value of x.
(xi) If AD= 4x-3, AE=8x -7, BC=3x-1 and CE=5x-3, find the value x.
(xii) If AD=2.5 cm, BD= =3.0 cm and AE=3.75 cm, find the length of AC.

Q. In the figure if

D E ∥ B C

and

A D = 3 x - 2

A E = 5 x - 4

B D = 7 X - 4

B D - 7 x - 5

AND

C E = 5 x - 3

. Find x.

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In the figure given, BD∥AE. If ¯¯¯¯¯¯¯¯CE=3 cm, what is the length of ¯¯¯¯¯¯¯¯AC?

The correct option is D 3Given BD||AECE=3 cmSince BD||AE and AC is transversal∠CAE=xSimilarly BD||AE and CE is transversal∠CEA=xIn △ACE∠CAE=∠CAE=x⟹AC=CE⟹AC=3 cm

In the figure given, $B D ∥ A E$ . If $¯ ¯¯¯¯¯¯ ¯ C E = 3$ cm, what is the length of $¯ ¯¯¯¯¯¯ ¯ A C$ ?

The correct option is D $3$
Given $B D | | A E C E = 3 c m$
Since $B D | | A E$ and $A C$ is transversal
$∠ C A E = x$
Similarly $B D | | A E$ and $C E$ is transversal
$∠ C E A = x$
In $△ A C E$
$∠ C A E = ∠ C A E = x$
$⟹ A C = C E$
$⟹ A C = 3 c m$