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The value of x is 15.
Solution:
Given ΔPQR ΔUTV.
<em>If two triangles are similar, then the corresponding parts are congruent.</em>
Do cross multiplication, we get
⇒ 14(x - 3) = 8(x + 6)
⇒ 14x - 42 = 8x + 48
Add 42 on both sides.
⇒ 14x = 8x + 90
Subtract 8x on both sides.
⇒ 6x = 90
Divide by 6 on both sides.
⇒ x = 15
The value of x is 15.
Properties of Similar Triangles
Please refer to the figure attached.
<span>Corresponding angles are congruent (same measure) So in the figure above, the angle P=P', Q=Q', and R=R'.
<span>
Corresponding sides are all in the same proportion. Above, PQ is twice the length of P'Q'. Therefore, the other pairs of sides are also in that proportion.</span></span>
Please refer to the figure attached.
<span>Corresponding angles are congruent (same measure) So in the figure above, the angle P=P', Q=Q', and R=R'.
<span>
Corresponding sides are all in the same proportion. Above, PQ is twice the length of P'Q'. Therefore, the other pairs of sides are also in that proportion.</span></span>