# Question Video: Applying the Side Comparison Theorem in Triangles to a Diagram Mathematics • 11th Grade

From the figure, fill in the blank with either >, <, or =: π΄πΆ οΌΏ π΄π΅.

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### Video Transcript

From the figure, fill in the blank with either greater than, less than, or equal to: π΄πΆ what π΄π΅.

In this question, we are given a figure containing the measures of some angles and a pair of parallel lines. We need to use this figure to compare the lengths of two line segments in the figure. To answer this question, letβs start by highlighting the two line segments whose lengths we want to compare. We can see that these line segments are both sides in triangle π΄π΅πΆ.

We can compare the side lengths in a triangle by using the side comparison theorem in triangles. To do this, we need to find the measures of the angles opposite these two sides. We will do this by using the fact that π΄πΆ and π΄π΅ are transversals of a pair of parallel lines. First, we note that π΄πΆ is a transversal of a pair of parallel lines. And we see that the angle at πΆ is the alternate interior angle of the given angle with measure 50 degrees.

Since alternate interior angles in a transversal of a pair parallel lines are congruent, we know that angle πΆ has measure 50 degrees. In the same way, we can see that π΄π΅ is a transversal of the pair of parallel lines. And the angle at π΅ is the corresponding angle to the angle of measure 70 degrees. So these two angles are congruent.

We can now compare the lengths of these two sides by using the side comparison theorem in triangles which tells us that in a triangle, the side opposite the angle with larger measure will be longer. In this triangle, we can see that the angle opposite side π΄πΆ has larger measure than the angle opposite side π΄π΅. This means that π΄πΆ is longer than π΄π΅.

Hence, the answer to this question is greater than, since π΄πΆ is greater than π΄π΅ because the measure of angle π΅ is greater than the measure of angle πΆ.