Question

name a. jurn loger date 12-12-25 hour 1
7.
given: line j is parallel to line k
and angles 4, 5, and 6 are all
congruent.
prove: ∠1≅∠2≅∠3
(5 points)
statements reasons
j || k given
∠4 ≅ ∠5 ≅ ∠6

Explanation:

Step1: Analyze triangle angles

In triangle with angles 4, 5, 6, since \( \angle 4 \cong \angle 5 \cong \angle 6 \), the triangle is equiangular. So each angle \( \angle 4=\angle 5=\angle 6 = 60^\circ \) (sum of triangle angles is \( 180^\circ \), \( 180\div3 = 60 \)).

Step2: Use parallel lines (corresponding angles)

Since \( j\parallel k \), \( \angle 1\cong\angle 4 \) (corresponding angles), \( \angle 3\cong\angle 6 \) (corresponding angles), \( \angle 2\cong\angle 5 \) (alternate interior angles).

Step3: Transitive property of congruence

From Step1 and Step2: \( \angle 1=\angle 4 = 60^\circ \), \( \angle 2=\angle 5 = 60^\circ \), \( \angle 3=\angle 6 = 60^\circ \). Thus, by transitive property, \( \angle 1\cong\angle 2\cong\angle 3 \).

Answer:

\(\angle 1\cong\angle 2\cong\angle 3\) is proven as shown above.