### Clarifications

*Clarification 1*: Instruction includes showing that the corresponding sides and the corresponding angles are congruent.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Coordinate Plane
- Origin
- Reflection
- Rigid Transformation
- Rotation
- Translation

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 8, students identified a single transformation given the preimage and the image and learned that when the transformation is a reflection, a rotation or a translation, those transformations preserve congruence, that is, the preimage is mapped onto a copy of itself. In Geometry, students determine whether two figures are congruent and justify their answers using a sequence of rigid motions. This leads to the definition of congruence in terms of rigid transformations.*(MTR.5.1)*

- When identifying the transformations in the sequence, specify the vertical and horizontal translations, center and angle of the rotation, clockwise or counterclockwise, line of reflection, when needed.
- Instruction includes describing the rigid transformations using words and using coordinates.
- It is important to identify corresponding parts between the preimage and the image leading to the congruence statement and the congruence of the corresponding parts (angles and sides).
- Instruction includes using examples to compare transformations preserving angle measures and distance versus transformations just preserving angle measures. Include situations where the preimage and the image are not congruent to show how rigid motions will fail mapping one figure onto the other.
*(MTR.4.1)*

### Common Misconceptions or Errors

- Students may have trouble seeing congruence when a reflection is needed because they limit their thinking to sliding a figure around without turning it over.

### Instructional Tasks

*Instructional Task 1 (MTR.3.1,*

*MTR.4.1*)- Two triangles on the coordinate plane are shown below.

- Part A. What transformation(s) could be applied to map triangle
*EBD*onto triangle*CBA*? - Part B. Once the transformation is completed, how can you determine if the two triangles are congruent?

### Instructional Items

*Instructional Item 1*

- Describe the sequence of transformations that could be used to prove that the two quadrilaterals shown are congruent.

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## MFAS Formative Assessments

Students are asked to use rigid motion to explain why the ASA pattern of congruence ensures triangle congruence.

Students are asked to use rigid motion to explain why the HL pattern of congruence ensures right triangle congruence.

Students are asked to use rigid motion to explain why the SAS pattern of congruence ensures triangle congruence.

Students are asked to use rigid motion to explain why the SSS pattern of congruence ensures triangle congruence.

In a diagram involving two parallel lines and a transversal, students are asked to use rigid motion to prove that alternate interior angles are congruent.

Students are asked to use the definition of congruence in terms of rigid motion to show that two triangles are congruent in the coordinate plane.

Students are asked to translate and rotate a triangle in the coordinate plane and explain why the pre-image and image are congruent.