What is the converse of alternate exterior angles theorem?

Converse of the Alternate Exterior Angles Theorem:

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

What is converse alternate angle test?

The converse of alternate angle theorem states that, If two lines and a transversal form alternate corresponding angles that are congruent, then the lines are parallel.

What is the inverse of the alternate interior angles theorem?

Alternate Interior Angles Theorem

The converse of this theorem, which is basically the opposite, is also a proven statement: if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

What is a converse theorem in geometry?

The converse of the Pythagorean Theorem states that if the square of the third side of a triangle is equivalent to the sum of its two shorter sides, then it must be a right triangle.

How do you prove converse of alternate interior angles theorem?

If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. Theorem 3.8: Alternate Interior Angles Converse: If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

What is the Alternate Exterior Angle Converse Theorem

Does every theorem have a converse?

a theorem obtained by reversing the roles of premise and conclusion of the initial (direct) theorem. Any theorem is the converse of its converse. Thus, a theorem and its converse are converses of each other.

Do alternate exterior angles add up to 180?

If the transversal cuts across parallel lines (the usual case) then exterior angles are supplementary (add to 180°). So in the figure above, as you move points A or B, the two angles shown always add to 180°.

What is the difference between a converse and a theorem in geometry?

As verbs the difference between theorem and converse

is that theorem is to formulate into a theorem while converse is (formal|intransitive) to talk; to engage in conversation.

What is the definition of a converse statement?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

What is converse in mathematical reasoning?

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P.

What is the converse of perpendicular transversal theorem?

Lesson Summary

The perpendicular transversal theorem tells you that in a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. The converse perpendicular transversal theorem tells you in a plane, if two lines are perpendicular to the same line, then they are parallel.

What is the converse of the consecutive same side interior angles theorem?

The converse of consecutive interior angle theorem states that if a transversal intersects two lines such that a pair of consecutive interior angles are supplementary, then the two lines are parallel.

Do alternate angles add up to 90?

If two parallel lines are joined by a line perpendicular to them, the resulting alternate interior angles will be 90 degrees.

What is the sum of alternate angles?

These angles are congruent. The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°. In the case of non – parallel lines, alternate interior angles don't have any specific properties.

How do you solve alternate exterior?

What is the converse of the above theorem?

How can you prove the converse of the above theorem. <br> " If a line in the plane of a circle is perpendicular to the radius at its endpoint on the circle, then the line is tangent of the circle ".

What is the symbolic form of converse?

A conditional statement is logically equivalent to its contrapositive. Converse: Suppose a conditional statement of the form "If p then q" is given. The converse is "If q then p." Symbolically, the converse of p q is q p.

What is the converse of the base angle theorem?

Converse of the Base Angles Theorem

If two angles of a triangle are congruent, then the sides opposite them are congruent.

What is alternate segment theorem?

The alternate segment theorem - Higher

The angle between a tangent and a chord is equal to the angle in the alternate segment.

What is converse of Mid Point theorem?

The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.

What is the converse of the angle bisector theorem?

Converse of Angle Bisector Theorem

In a triangle, if the interior point is equidistant from the two sides of a triangle then that point lies on the angle bisector of the angle formed by the two line segments.