Question

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if parallel lines a and b are cut by transversal t, which pair of angles are corresponding angles?
options:
∠3 and ∠5
∠2 and ∠6
∠2 and ∠4
∠1 and ∠3

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are in the same position relative to the parallel lines and the transversal.

Step2: Analyze Each Option

• Option 1: $\angle 3$ and $\angle 5$: $\angle 3$ is interior, $\angle 5$ is interior but alternate, not corresponding.
• Option 2: $\angle 2$ and $\angle 6$: $\angle 2$ is upper - left of transversal on line $a$, $\angle 6$ is upper - left of transversal on line $b$. Same position, so corresponding.
• Option 3: $\angle 2$ and $\angle 4$: Different positions (vertical and opposite - side), not corresponding.
• Option 4: $\angle 1$ and $\angle 3$: Vertical angles, not corresponding.

Answer:

$\boldsymbol{\angle 2}$ and $\boldsymbol{\angle 6}$ (the option with $\angle 2$ and $\angle 6$)