4/22/2021 0 Comments Lesson Guide Angle Relationships
And, of course, R Y L pairs off as the alternate interior angle of T L Y.You may even have learned about straight and reflex angles, but if you are angling to learn even more, you can investigate many other kinds of angles like exterior and interior angles.You can learn about congruent, adjacent, vertical, corresponding, and alternating angles, too.We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles.
When two parallel lines are intersected by a transversal, complex angle relationships form, such as alternating interior angles, corresponding angles, and so on. ![]() ![]() So these two 35 angles are congruent, even if they are not identically presented, and are formed with different constructions. Any two angles sharing a ray, line segment or line are adjacent. In the following drawing, L i n e J C intersects L i n e O K, creating four adjacent pairs and intersecting at P o i n t Y. Here the word vertical means relating to a vertex, not up and down. Vertical angles are opposite angles; they share only their vertex point. Adjacent angles share more than the vertex; they share a common side to an angle. The more restrictive our intersecting lines get, the more restrictive are their angle relationships. When a line crosses two parallel lines (a transversal), a whole new level of angle relationships opens up. Point Y is along AR; Point L is along TO; the whole figure spells ADROITLY in a circular way. Angles that have the same position relative to one another in the two sets of four angles (four at the top, L i n e A R; four at the bottom, L i n e T O ) are corresponding angles. When the corresponding angles are on parallel lines, they are congruent. An exterior angle among line constructions (not polygons) is one that lies outside the parallel lines. In our figure above, A Y D and T L I are consecutive exterior angles. Alternate exterior angles are on opposite sides of the transversal (thats the alternate part) and outside the parallel lines (thats the exterior part). Can you find the two pairs of alternate exterior angles in our drawing. Just as with exterior angles, we can have consecutive interior angles and alternate interior angles. They lend themselves to the Alternate Interior Angles Theorem, which states that congruent alternate interior angles prove parallel lines (much as the Alternate Exterior Angles Theorem did).
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