Geometry 3.1, 3.2 and 3.3 Brit Caswell.

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Presentation transcript:

Geometry 3.1, 3.2 and 3.3 Brit Caswell

Parallel lines are coplanar lines that do not intersect Parallel lines are coplanar lines that do not intersect. This symbol means “is parallel to”.

Parallel planes are planes that do not intersect.

Skew lines are noncoplanar; they are not parallel and do not intersect.

A transversal is a line that intersects two or more coplanar lines at distinct points.

If And Only If Statements If and only if statements (iff) are statements that are true if one side of the statement is true. “If it is raining outside, I will take my umbrella.” “If I have my umbrella, _______________.” “I will take my umbrella with me if and only if it is raining.”

Alternate Interior Angles Alternate Interior Angles are nonadjacent interior angles that lie on an opposite side of the transversal. Theorem 3.1 states that the lines crossed by a transversal are parallel if and only if the AIA are congruent.

Same-side Interior Angles Same-side interior angles are interior angles that lie on the same side of the transversal. Two lines being crossed by a transversal are parallel if and only if the SSIA are supplementary.

Corresponding Angles Corresponding angles lie on the same side of the transversal and in corresponding positions. Theorem 3.2 states that corresponding angles are congruent if and only if the lines being crossed by the transversal are parallel.

Alternate Exterior Angles Alternate exterior angles are nonadjacent exterior angles that lie on opposite sides of the transversal. Theorem 3.3 states that the transversal crosses two parallel lines if and only if the AEA are congruent.

Postulate If two parallel lines are crossed by a transversal, then their corresponding angles are congruent.

I Do Using your knowledge of the relationships of angles shown today, determine the value of the marked angles. 1 4 2 5 3 45˚

We Do (Pg 145, #37-41) Determine whether each statement is always, sometimes, or never true. Two parallel lines are coplanar Two skew lines are coplanar Two planes that do not intersect are parallel Two lines that lie in parallel planes are parallel Two lines in intersecting planes are skew

You Do (Exit Ticket) Using your knowledge of the relationships shown over the past few days, determine the values of the marked angles, if possible. 3 130˚ 1 4 5 2

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