Consider the figure shown where $j | | k | | l$ .

If XY = YZ and TU = 3 cm, what is the length of UV?

3 cm

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6 cm

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9 cm

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Cannot be determined

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Solution

The correct option is A 3 cm
The intercept theorem states that if there are three or more parallel lines and the intercepts made by them on one transversal are equal, then the intercepts made by them on any other transversal are also equal.

It is given that $j | | k | | l$ .
Also, $X Y = Y Z$
Now, r and p are transversal.
Thus, using the intercept theorem, we have, $T U = U V = 3$ cm.
So, the correct answer is option (a).

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Question 48

If $Δ P Q R$ is congruent to $Δ S T U$ as shown in the given figure, then what is the length of TU?

a) 5 cm
b) 6 cm
c) 7 cm
d) Cannot be determined

∠ R P Q

∠ U V S

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