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You cannot possibly draw parallel lines with a transversal that creates a pair of corresponding angles, each measuring 181°. If two corresponding angles of a transversal across parallel lines are right angles, all angles are right angles, and the transversal is perpendicular to the parallel lines. Because of the vertical angles theorem, angle 4 and 8 and also measure 123°.

What does that tell you about the lines cut by the transversal?Īnd now, the answers (try your best first!):Īngle 5 also measures 123°.

If they are false, find a counterexample. b) Determine if the statements from part a are true or false. a) Find the converse, inverse, and contrapositive. Use the statement: If n > 2, then n2 > 4. You learn that corresponding angles are not congruent. Finding the Converse, Inverse, and Contrapositivive. Imagine a transversal cutting across two lines. If two corresponding angles of a transversal across parallel lines are right angles, what do you know about the figure?Ĭan you possibly draw parallel lines with a transversal that creates a pair of corresponding angles, each measuring 181°? You can use the Corresponding Angles Theorem even without a drawing. Looking at our BOLD MATH figure again, and thinking of the Corresponding Angles Theorem, if you know that angle 1 measures 123°, what other angle must have the same measure? If c 2 a 2 + b 2, then the triangle is a. Suppose a, b, and c are sides of a triangle and c is the longest side of the triangle. If the lines cut by the transversal are not parallel, then the corresponding angles are not equal. Basically, the converse of the Pythagorean theorem states that whenever the sum of the squares of two sides (legs) equal to the square of the third side (hypotenuse) of the triangle, the triangle is a right triangle. Since the corresponding angles are shown to be congruent, you know that the two lines cut by the transversal are parallel.