Exploring Similar and Congruent Triangles
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Take a look at ABC and DEF and compare them. What do they have in common? What is different about them?
You may have noticed that they have equivalent angles. , , and . Now, the side lengths are not the same, but what if we take a look at the ratios between the side lengths. Take a moment to calculate , , and round your answer to two decimal places. What do you notice?
You may have noticed that they are all equal! This is true for all triangles that share equivalent interior angles. Move points B and E around to get new dimensions and calculate the above ratios again. Did you get the same thing?
Are you able to make it so that each triangle has the same side lengths?
Summary
When two triangles have the same interior angles, we say that they are similar triangles.
Properties of Similar Triangles
- Interior angles of both triangles are the same
- The ratios of their corresponding sides are equal.