Back to Prove theorems about lines — Problem 3 · Task Set 9

Exercises: Prove Theorems About Lines and Angles

Work through each section in order. For proof problems, show each step with its justification. Express angle measures in degrees.

Grade 9·21 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-co-c-9

Work through problems with immediate feedback

Fluency Practice

Apply the theorems directly. Identify angle relationships and find missing measures.

$Two parallel lines l and m cut by a transversal, with angles 1-4 at line l and angles 5-8 at line m.$

Line $l$ is parallel to line $m$ . A transversal crosses both lines, creating eight angles labeled $\angle 1$ through $\angle 8$ (angles $\angle 1$ – $\angle 4$ at the intersection with $l$ ; angles $\angle 5$ – $\angle 8$ at the intersection with $m$ , in matching positions). Which pair is a pair of alternate interior angles?

$\angle 1$ and $\angle 5$

$\angle 4$ and $\angle 5$

$\angle 4$ and $\angle 6$

$\angle 3$ and $\angle 6$