Are the triangles below similar?
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Are the triangles below similar?
To solve this problem, we'll determine if the triangles and are similar using the Side-Side-Side (SSS) similarity criterion.
Step 1: Identify the sides of both triangles:
For , the side lengths are , , and .
For , the side lengths are , , and .
Step 2: Calculate the ratios of the corresponding sides:
Step 3: Verify similarity:
All three ratios are equal, so by the SSS criterion, the triangles are similar.
Therefore, the triangles and are similar.
Yes
The two parallelograms above are similar. The ratio between their sides is 3:4.
What is the ratio between the the areas of the parallelograms?
When all ratios equal 1, it means the triangles are congruent! Congruent triangles are a special case of similar triangles where the scale factor is 1 (same size and shape).
Match sides by position and length. In this problem, both triangles have sides of 5, 4, and 4, so the 5's correspond, and the 4's correspond to each other.
No! The SSS criterion says if all three side ratios are equal, the triangles are automatically similar. You don't need to measure or calculate angles.
The triangles would still be similar! For example, if all ratios equaled , the triangles would be similar with a scale factor of .
No! For SSS similarity, you need all three corresponding side ratios to be equal. If even one ratio is different, the triangles are not similar.
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