These two scalene triangles are similar with a scale of 2:3. What is true about these figures?
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When two triangles are similar, it means that they have the same shape, but possibly different sizes. In this case, the two scalene triangles are similar with a scale of 2:3.
To determine what is true about these figures, we can consider the properties of similar triangles:
1. Corresponding angles are congruent: This means that the corresponding angles in both triangles are equal. For example, if angle A in one triangle corresponds to angle X in the other triangle, angle A and angle X will have the same measure.
2. Corresponding sides are proportional: This means that the ratio of the lengths of any corresponding sides in both triangles will be the same. In this case, since the scale of similarity is 2:3, it means that for any corresponding sides, the ratio of their lengths in the first triangle to the lengths in the second triangle will be 2:3.
For example, if side AB in the first triangle corresponds to side PQ in the second triangle, the ratio of AB to PQ will be 2:3. Similarly, the ratio of BC to QR and AC to PR will also be 2:3.
These are the general properties that hold true for any pair of similar triangles. However, without specific information about the triangles, we cannot make any additional conclusions about their angles or side lengths.
their perimeters are also in the ratio 2:3
their areas are in the ratio 4:9
All the corresponding angles are congruent.