Back to Prove theorems about lines — Problem 1 · 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.

$Two intersecting lines at point O with angles 1, 2, 3, 4 labeled clockwise around the intersection.$

Two lines intersect at point $O$ , forming angles $\angle 1$ , $\angle 2$ , $\angle 3$ , and $\angle 4$ arranged around $O$ (numbered clockwise). $\angle 1$ and $\angle 3$ are vertical angles; $\angle 2$ and $\angle 4$ are vertical angles.

Write the key steps of a proof that $\angle 1 \cong \angle 3$ . Name the justification for each step.