Cogito
Grade 8 Math · Chapter 1 · Lesson 2
Congruence
Same shape, same size, wherever it sits.
10 problems · about 18 minutes · 8.G.A.2
What this lesson teaches
The child decides whether two figures are congruent by finding a sequence of rigid motions.
- Congruent means one can be carried onto the other by rigid motions.
- Several moves in sequence are allowed.
- Matching sides and angles are therefore equal.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Moving a Shape Without Changing It: (2, 9) reflected across the vertical axis. New first coordinate?
Answer -2
Why (−2, 9).
Review — Moving a Shape Without Changing It: What does a rigid motion preserve?
Answer Lengths and angles.
Why Lengths and angles survive; position does not.
Warm Up
Straightforward practice. Get the method working first.
4 problemsCongruent shapes, one side is 15. The matching side?
Answer 15
Why 15.
How is congruence defined?
Answer One can be carried onto the other by rigid motions.
Why Congruence is defined by a sequence of rigid motions.
Congruent shapes, one side is 12. The matching side?
Answer 12
Why Unchanged.
Congruent shapes, one angle is 90. The matching angle?
Answer 90
Why Unchanged.
Build It Up
The same ideas with more to keep track of.
2 problemsCan a reflection be part of proving congruence?
Answer Yes.
Why Any rigid motions are allowed.
Does a dilation preserve congruence?
Answer No. It changes lengths.
Why It is not a rigid motion.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Matching Side: Two congruent triangles. One has a side of 7. What is the matching side on the other?
Answer 7
Why 7.
The Matching Angle: Two congruent shapes. One has an angle of 55 degrees. What is the matching angle?
Answer 55 degrees
Why 55 degrees.