Lesson 21: Applying Basic Geometric Concepts

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Lesson 21: Applying Basic Geometric Concepts
Obj: to understand & apply concepts involving angles and lines

EUCLID of ALEXANDRIA The Father of Geometry wrote “Elements”
He lived around 300 BC in Greece “Elements” is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.

Geometric Terms Perpendicular Lines: Lines that intersect to form a right or 90° angle. The symbol means is perpendicular to.

Geometric Terms Parallel Lines: lines in the same plane that do not intersect. The symbol // means is parallel to. The arrows on the lines indicates that the lines are parallel also.

Geometric Terms Transversal: a line that intersects at least two other lines at different points. When a pair of lines are cut by a transversal there are special angle pairs that are formed.

Special Angle Pairs Complementary Angles: a pair of angles that has a sum of 90°.

Special Angle Pairs Supplementary Angles: A pair of angles that has a sum of 180°

Special Angle Pairs Adjacent Angles: A pair of angles that share a common side and a common vertex.

Special Angle Pairs Linear Pair: Special angle pair that forms a straight line. The angles have a sum of 180°. The angles have to be adjacent.

Special Angle Pairs Vertical Angles: Special angle pair formed by intersecting lines. The angles are congruent or have the same measure.

Interior Angles: angles that are in between the lines.
Special Angle Pairs Interior Angles: angles that are in between the lines.

Exterior Angles: angles that are outside the lines
Special Angle Pairs Exterior Angles: angles that are outside the lines

When the lines are parallel, then the angles are congruent.
Special Angle Pairs Alternate Interior Angles: Special angle pair formed by two lines cut by a transversal. They are interior angles on opposite sides of the transversal. One angle is on the top and the other angle is on the bottom. They form the letter Z. When the lines are parallel, then the angles are congruent.

When the lines are parallel, then the angles are congruent.
Special Angle Pairs Alternate Exterior Angles: Special angle pair formed by two lines cut by a transversal. They are exterior angles on opposite sides of the transversal. One angle is on the top and the other angle is on the bottom. When the lines are parallel, then the angles are congruent.

When the lines are parallel, then the angles are congruent.
Special Angle Pairs Corresponding Angles: Special angle pair formed by two lines cut by a transversal. One angle is an exterior angle and one angle is and interior angle. Both angles are on the same side of the transversal. One is on the top and the other is on the bottom. When the lines are parallel, then the angles are congruent.