Unit 2, Lesson 1
Congruent Parts, Part 1
Geometry
1.1
Warm-up
Notice and Wonder: A Dart
What do you notice? What do you wonder?
1.2
Activity
If We Know This, Then We Know That
Triangle
- Find a sequence of rigid motions that takes triangle
to triangle . - What is the image of segment
after that transformation? - Explain how you know those segments are congruent.
- Justify that angle
is congruent to angle .
Student Lesson Summary
If a part of the image matches up with a part of the original figure, we call them corresponding parts. The part could be an angle, point, or side. We can find corresponding angles, corresponding points, or corresponding sides.
If two figures are congruent, then there is a rigid transformation that takes one figure onto the other. The same rigid transformation can also be applied to individual parts of the figure, such as segments and angles, because rigid transformations act on every point on the plane. Therefore, the corresponding parts of two congruent figures are congruent to each other.
Using a translation and a rotation we can take quadrilateral
- Angle
is congruent to angle . - Segment
is congruent to segment . - Angle
is congruent to angle . - Segment
is congruent to segment .
corresponding parts
Corresponding parts are the matching parts of an original figure and its scaled copy that are in the same relative positions. The parts could be points, segments, angles, or distances. When two figures are congruent, all of their corresponding parts are congruent.
For example, in triangles
- Point
corresponds to point . - Segment
corresponds to segment . - Angle
corresponds to angle .
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