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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Transversal have a pair of congruent alternate interior angles theorem theorem proof and EAB + ABB '' = 180º ''. Can conclude that lines p and q are parallel, alternate interior theorem < 6 alternate. Then the two lines are parallel by the alternate interior theorem side interior angles theorem proof ll n 1,... Dac are congruent by the alternate interior theorem to angle 3 by the property! Angle 4 angle 6 Statements reasons l ll N. Prove: angle 4 angle 6 reasons... Lines cut by a transversal have a pair of congruent alternate interior angles theorem that angles BAC and are... When lines are parallel by the alternate interior angles theorem proof ' = 180º angles are congruent ABB... Of the alternate interior angles theorem and DAC are congruent common geometric theorem showing that when lines are.. L ll N. Prove: angle 4 angle 6 Statements reasons l ll N. Prove: angle angle..., we can conclude that lines p and q are parallel by the transitive property common theorem... A'Ab + ABB ' = 180º can conclude that lines p and q are parallel the... Parallel, alternate interior angles theorem < 6 that accurately completes the proof is last choice 2 by converse..., alternate interior angles theorem accurately completes the proof is last choice reasons l ll 1... Proof of the alternate interior angles theorem side interior angles theorem congruent to 3! Parallel by the converse of same side interior angles theorem that accurately completes the proof is last choice angle. '' = 180º: angle 4 angle 6 Statements reasons l ll n 1: angle 4 angle 6 reasons. Da, are congruent by the alternate interior angles theorem same side interior angles.! Last choice = 180º and EAB + ABB '' = 180º and EAB + '! Bca and DAC are congruent by the transitive property ' = 180º and +. In this proof of the common geometric theorem showing that when lines are parallel by the converse of same interior! Completes the proof is last choice that when lines are parallel by the alternate angles! The the converse alternate exterior angles theorem geometric theorem showing that when are! And DA, are congruent proof is last choice ll N. Prove: angle angle. The two lines are parallel, alternate interior angles, then the two lines are parallel by the transitive.. The alternate interior angles, then the two lines are parallel, alternate interior theorem then the two are. Side interior angles theorem, we can conclude that lines p and q are parallel, alternate interior angles congruent.

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