Parallel Lines Cut by a Transversal: Angle Relationships

**Naming the Angles** — Study the diagram of two parallel lines cut by a transversal. Eight angles are formed and numbered $1$ through $8$. ```geometry {"figureType":"transversal","angle":55,"lineLabels":["m","n"],"transversalLabel":"t","showAngles":[1,2,3,4,5,6,7,8],"angleLabels":{"1":"55°"},"parallelMarks":true,"title":"Parallel Lines m and n Cut by Transversal t"} ``` Using the diagram and your color-coded reference card, complete the table: | Angle Pair | Names | Relationship | Are they equal or supplementary? | |---|---|---|---| | Corresponding | ∠1 and ∠___ | Same side, same position | | | Alternate Interior | ∠3 and ∠___ | Between the lines, opposite sides | | | Alternate Exterior | ∠2 and ∠___ | Outside the lines, opposite sides | | | Co-Interior (Same-Side Interior) | ∠4 and ∠___ | Between the lines, same side | | **Sentence frame:** "Angles ___ and ___ are ___ angles. Since lines $m$ and $n$ are parallel, they are ___."

**Patty Paper Check** — Use tracing paper (or the diagram below) to test whether the angle pairs you identified in Task 1 are truly congruent. ```geometry {"figureType":"transversal","angle":55,"lineLabels":["m","n"],"transversalLabel":"t","showAngles":[1,3,5,7],"angleLabels":{"1":"55°","3":"125°","5":"55°","7":"125°"},"shadedAngles":[1,5],"arcTicks":{"1":1,"5":1,"3":2,"7":2},"parallelMarks":true,"title":"Congruent Alternate Interior & Corresponding Angles"} ``` **Directions (choose one):** - **Kinesthetic:** Trace ∠1 on patty paper. Slide the tracing down to ∠5. Do they match? Record what you notice. - **Visual:** Look at the arc-tick marks on the diagram. Which angles share the same number of ticks? What does that tell you? - **Written:** In one or two sentences, explain WHY alternate interior angles are congruent when lines are parallel. Then answer: If $m\angle 1 = 55°$, state the measure of every other labeled angle and give the relationship name.