Similar Figures

When two figures are similar, the ratios of corresponding sides will be equal.

EXAMPLE 2: 

SOLUTION:  AC corresponds to QP and BC corresponds to RP, so we can use the following proportion:

We can solve this by cross-multiplying:

Now factor:

This has solutions x = 8 and x = –1. 

Since x is a side of a triangle, it cannot be negative, so the only meaningful solution is x = 8.

Now side QR corresponds to side AB.  Since AB = 2(8) – 4 = 12, we can use a ratio to find QR. 

To get the ratio, we also need side QP since that corresponds to AC and we know AC = 8.

QP = 8 + 4 = 12.  Now we can find QR:

Cross-multiplying:  8QR = 144,  so QR = 18

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