# Lesson 5

Points, Segments, and Zigzags

### Lesson Narrative

In previous lessons, students began justifying why points coincide in figures with congruent parts. These justifications can be long since proving figures are congruent in a rigorous way requires great attention to detail. In this lesson, students will attend to precision (MP6) while proving all points are congruent and all segments of the same length are congruent. This will build toward proving triangles congruent in the subsequent lessons. In those proofs, students can skip the steps they prove here. This allows them to start by saying a transformation exists to take a segment to a congruent segment and focus their attention on using the remaining information to prove the triangles congruent.

### Learning Goals

Teacher Facing

• Prove (in writing) two segments are congruent if and only if they have the same length.

### Student Facing

• Let’s figure out when segments are congruent.

### Required Preparation

Add to the display of sentence frames for proofs. An example template is provided in the blackline masters for this lesson.

### Student Facing

• I can write a proof that segments of the same length are congruent.

Building On

### Glossary Entries

• corresponding

For a rigid transformation that takes one figure onto another, a part of the first figure and its image in the second figure are called corresponding parts. We also talk about corresponding parts when we are trying to prove two figures are congruent and set up a correspondence between the parts to see if the parts are congruent.

In the figure, segment $$AB$$ corresponds to segment $$DE$$, and angle $$BCA$$ corresponds to angle $$EFD$$.

### Print Formatted Materials

For access, consult one of our IM Certified Partners.