Let l;m be two lines cut by a transversal t … A proof of the common geometric theorem showing that when lines are parallel, alternate interior angles are congruent. Proof. It is congruent to itself by the Reflexive Property of Equality. Figure 1: Congruent alternate interior angles imply parallel Theorem 1.1 (Alternate Interior Angle Theorem). So, we can conclude that lines p and q are parallel by the converse alternate exterior angles theorem. Give the missing reasons in this proof of the Alternate Interior Angles Theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. _____. 1. Angles BCA and DAC are congruent by the Alternate Interior Theorem. If two distinct lines cut by a transversal have a pair of congruent alternate interior angles, then the two lines are par-allel. angle angle 2 b.? angle 6 angle 4 c ? Use the figure and flowchart proof to answer the question:Which theorem accurately completes Reason A? Which sentence accurately completes the proof? Same-Side Interior Angles Theorem. Statements . We see that Angle 2 is congruent to Angle 3 by the alternate interior angles theorem. Converse of the alternate interior angles theorem 1 m 5 m 3 given 2 m 1 m 3 vertical or opposite angles 3 m 1 m 5 using 1 and 2 and transitive property of equality both equal m 3 4 1 5 3 the definition of congruent angles 5 ab cd converse of the corresponding angles theorem. The sentence that accurately completes the proof is last choice. Given: L ll N. Prove:<4 congruent <6. Given angle 2 angle 6 a ? It states that Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Proving that angles are congruent: If a transversal intersects two parallel lines, then the following angles are congruent (refer to the above figure): Alternate interior angles: The pair of angles 3 and 6 (as well as 4 and 5) are alternate interior angles. New questions in Mathematics. Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles … By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent. Since the By substitution, A'AB + ABB' = 180º and EAB + ABB'' = 180º. Converse of Alternate Interior Angles Theorem Proof. Give the missing reasons in this proof of the alternate interior angles theorem. L||n Given: Prove:angle 4 angle 6 Statements Reasons l ll n 1. solving systems of linear inequalities Please help me answer truth or false for questions The converse of same side interior angles theorem proof. 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