How to find comparison of an angle
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Look at the triangle below. The sides of the triangle are given. Can you determine which angle is the largest? The largest angle will be opposite 18 because that is the longest side. Similarly, the smallest angle will be opposite 7, which is the shortest side.
This idea is actually a theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
The converse is also true: If one angle in a triangle is larger than another angle in that triangle, then the side opposite the larger angle will be longer than the side opposite the smaller angle.
We can extend this idea into two theorems that help us compare sides and angles in two triangles If we have two congruent triangles △ABC and △DEF, marked below:
Therefore, if AB=DE, BC=EF, and m∠B=m∠E, then AC=DF.
Now, let’s make m∠B>m∠E. Would that make AC>DF? Yes. This idea is called the SAS Inequality Theorem.
This idea is actually a theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.
The converse is also true: If one angle in a triangle is larger than another angle in that triangle, then the side opposite the larger angle will be longer than the side opposite the smaller angle.
We can extend this idea into two theorems that help us compare sides and angles in two triangles If we have two congruent triangles △ABC and △DEF, marked below:
Therefore, if AB=DE, BC=EF, and m∠B=m∠E, then AC=DF.
Now, let’s make m∠B>m∠E. Would that make AC>DF? Yes. This idea is called the SAS Inequality Theorem.
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