# Lesson 2

Congruent Parts, Part 2

• Let’s name figures in ways that help us see the corresponding parts.

### 2.1: Math Talk: Which Are Congruent?

Each pair of figures is congruent. Decide whether each congruence statement is true or false.

Triangle $$ABC$$ is congruent to triangle $$FED$$.

Quadrilateral $$PZJM$$ is congruent to quadrilateral $$LYXB$$.

Triangle $$JKL$$ is congruent to triangle $$QRS$$.

Pentagon $$ABCDE$$ is congruent to pentagon $$PQRST$$.

### 2.2: Which Triangles Are Congruent?

Here are three triangles.

1. Triangle $$PQR$$ is congruent to which triangle? Explain your reasoning.
2. Show a sequence of rigid transformations that takes $$PQR$$ to that triangle. Draw each step of the transformation.
3. Explain why there can’t be a rigid transformation to the other triangle.

### 2.3: Are These Parts Congruent?

1. Triangle $$ABD$$ is a rotation of triangle $$CDB$$ around point $$E$$ by $$180^{\circ}$$. Is angle $$ADB$$ congruent to angle $$CDB$$? If so, explain your reasoning. If not, which angle is $$ADB$$ congruent to?

2. Polygon $$HIJKL$$ is a reflection and translation of polygon $$GFONM$$. Is segment $$KJ$$ congruent to segment $$NM$$? If so, explain your reasoning. If not, which segment is $$NM$$ congruent to?

3. Quadrilateral $$PQRS$$ is a rotation of polygon $$VZYW$$. Is angle $$QRS$$ congruent to angle $$ZYW$$? If so, explain your reasoning. If not, which angle is $$QRS$$ congruent to?

Suppose quadrilateral $$PQRS$$ was both a rotation of quadrilateral $$VZYW$$ and also a reflection of quadrilateral $$YZVW$$. What can we conclude about the shape of our quadrilaterals? Explain why.

### Summary

Naming congruent figures so it’s clear from the name which parts correspond makes it easier to check whether 2 figures are congruent and to use corresponding parts. In this image, segment $$AB$$ appears to be congruent to segment $$DE$$. Also, segment $$EF$$ appears to be congruent to segment $$BC$$. So, it makes more sense to conjecture that triangle $$ABC$$ is congruent to triangle $$DEF$$ than to conjecture triangle $$ABC$$ is congruent to triangle $$FDE$$.

If we are told quadrilateral $$MATH$$ is congruent to quadrilateral $$LOVE$$, without even looking at the figures we know:

• Angle $$M$$ is congruent to angle $$L$$.
• Angle $$A$$ is congruent to angle $$O$$.
• Angle $$T$$ is congruent to angle $$V$$.
• Angle $$H$$ is congruent to angle $$E$$.
• Segments $$MA$$ and $$LO$$ are congruent.
• Segments $$AT$$ and $$OV$$ are congruent.
• Segments $$TH$$ and $$VE$$ are congruent.
• Segments $$HM$$ and $$EL$$ are congruent.

Quadrilaterals $$MATH$$ and $$LOVE$$ can be named in many different ways so that they still correspond—such as $$ATHM$$ is congruent to $$OVEL$$ or $$THMA$$ is congruent to $$VELO$$. But $$ATMH$$ is congruent to $$LOVE$$ means there are different corresponding parts. Note that quadrilateral $$MATH$$ refers to a different way of connecting the points than quadrilateral $$ATMH$$.

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