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