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
Answer: Angle 6 ≅ Angle 1, Angle 5 ≅ Angle 3, Angle 4 ≅ Angle 2.
Reason: Lines a and b cut the parallel lines p and q, so the angles formed by the same transversal on the two parallels are corresponding (hence congruent): angle 5 ≅ angle 3 and angle 4 ≅ angle 2. The two triangles share the vertex where a and b meet, so the apex angles (1 and 6) are congruent. Thus the last set of statements is true.
Reason: Lines a and b cut the parallel lines p and q, so the angles formed by the same transversal on the two parallels are corresponding (hence congruent): angle 5 ≅ angle 3 and angle 4 ≅ angle 2. The two triangles share the vertex where a and b meet, so the apex angles (1 and 6) are congruent. Thus the last set of statements is true.
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