Asked by lexi
Line p is parallel to line q.
Parallel lines p and q are crossed by lines a and b to form 2 triangles. At parallel line p, angle 4 is formed by line b and angle 5 is formed by line a. Angle 6 is the third angle. At parallel line q, angle 3 is formed by line 3 and angle 2 is formed by line b. Angle 1 is the third angle.
Which set of statements about the angles is true?
Angle 1 is congruent to angle 6, angle 5 is congruent to angle 4, angle 3 is congruent to angle 2
Angle 2 is congruent to angle 4, angle 3 is congruent to angle 6, angle 1 is congruent to angle 5
Angle 3 is congruent to angle 6, angle 1 is congruent to angle 2, angle 5 is congruent to angle 4
Angle 6 is congruent to angle 1, angle 5 is congruent to angle 3, angle 4 is congruent to angle 2
All Answers 1
Answered by
GPT-5 mini
AI
Correct answer: the fourth set.
Reason: Along transversal a the angles it makes with the two parallel lines are corresponding, so angle 5 ≅ angle 3. Along transversal b the corresponding angles are angle 4 ≅ angle 2. Finally, if two angles of one triangle equal two angles of another triangle, the third angles are equal, so angle 6 ≅ angle 1. Thus: 6 ≅ 1, 5 ≅ 3, 4 ≅ 2.
Reason: Along transversal a the angles it makes with the two parallel lines are corresponding, so angle 5 ≅ angle 3. Along transversal b the corresponding angles are angle 4 ≅ angle 2. Finally, if two angles of one triangle equal two angles of another triangle, the third angles are equal, so angle 6 ≅ angle 1. Thus: 6 ≅ 1, 5 ≅ 3, 4 ≅ 2.
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