(a) Rigid Transformation: A rotation of 180 degrees clockwise is the transformation mapping ∆ABC onto ∆DBE. (b) Corresponding Sides and Angles: Corresponding angles (ACB, BAC, ABC) match with (BED, BDE, EBD), and corresponding sides (AC, AB, CB) match with (DE, BD, EB). (c) Summary of Corresponding Sides and Angles: AC corresponds to DE, AB corresponds to BD, CB corresponds to EB; ∠ACB corresponds to ∠BED, ∠ABC corresponds to ∠EBD, ∠BAC corresponds to ∠BDE.
(a) Rigid Transformation
The rigid transformation that can be used to map ∆ABC onto ∆DBE is a rotation. Specifically, a rotation of 180 degrees in the clockwise direction will map ∆ABC onto ∆DBE.
(b) Corresponding Sides and Angles
For the corresponding sides and angles:
Angles:
- ∠ACB corresponds to ∠BED
- ∠BAC corresponds to ∠BDE
- ∠ABC corresponds to ∠EBD
Sides:
- Side AC corresponds to side DE
- Side AB corresponds to side BD
- Side BE corresponds to side CB
(c) Summary of Corresponding Sides and Angles
Corresponding Sides:
- AC corresponds to DE
- AB corresponds to BD
- CB corresponds to EB
Corresponding Angles:
- ∠ACB corresponds to ∠BED
- ∠ABC corresponds to ∠EBD
- ∠BAC corresponds to ∠BDE
Additional Information
A rigid transformation (or isometry) is a transformation that preserves the sides and angles of plane figures. The three types of rigid transformations are:
1. Translation
2. Reflection
3. Rotation
In this case, a rotation is employed.
Explanation of Rigid Transformation
If we perform a rotation of 180 degrees in the clockwise direction, the transformation ensures that the corresponding sides and angles of ∆ABC align precisely with those of ∆DBE.
Recap of Corresponding Angles and Sides
- Angles:
- ∠ACB corresponds to ∠BED
- ∠BAC corresponds to ∠BDE
- ∠ABC corresponds to ∠EBD
- Sides:
- Side AC corresponds to side DE
- Side AB corresponds to side BD
- Side CB corresponds to side EB
The complete question is:
∆ABC is transformed to ∆DBE
(a) which rigid transformation can be used to map ∆ABC on to ∆DBE
(b) What is true about the corresponding sides and angles of the image and the preimage? Explain.
(c) Identify the corresponding sides and angles of the image and the preimage