## alternate interior angles theorem proof

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