The correct option to explain how the SAS criterion can be used to prove similarity in two triangles is:
c. If two corresponding side lengths of each triangle are given and are proportional, with a proven included angle measure, the triangles are similar.
Explanation:
The SAS (Side-Angle-Side) similarity criterion states that if in two triangles, the lengths of two sides are in proportion and the included angle (the angle between the two sides) is equal, then the two triangles are similar.
Here’s a breakdown of the usage of the SAS criterion:
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Proportional Sides: Begin with two triangles, say triangle ABC and triangle DEF. If the lengths of two pairs of corresponding sides are in proportion (for example, AB/DE = AC/DF), this condition must hold true.
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Equal Included Angle: Next, you must demonstrate that the included angles between these pairs of sides are equal (for instance, angle B = angle E). This means that the angle formed by side AB and AC in triangle ABC is equal to the angle formed by side DE and DF in triangle DEF.
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Conclusion: Given these two conditions (proportional sides and equal included angle), you can conclude that triangle ABC is similar to triangle DEF (denoted as triangle ABC ~ triangle DEF). This similarity implies that corresponding angles are equal and corresponding sides are in proportion.
Thus, response c accurately captures the essence of the SAS similarity criterion.
3 answers