Congruence Through Transformations

Same shape means one can be moved onto the other.

12 problems · about 21 minutes · G-CO.B.6, G-CO.B.7

What this lesson teaches

The student defines congruence via rigid transformations and identifies corresponding parts.

Congruent means a sequence of rigid transformations maps one figure onto the other.
Corresponding sides and angles of congruent figures are equal.
The order of letters in a congruence statement states the correspondence.

Straightforward practice. Get the method working first.

5 problems

ABC congruent to DEF with AB = 7. What is DE?
Answer 7
Why 7.
What does it mean for two figures to be congruent?
Answer Rigid transformations carry one exactly onto the other.
Why One can be moved exactly onto the other.
ABC congruent to DEF with BC = 9. What is EF?
Answer 9
Why BC matches EF.
Same triangles with angle A = 70°. What is angle D?
Answer 70
Why A matches D.
Same triangles with AC = 12. What is DF?
Answer 12
Why A matches D and C matches F.

The same ideas with more to keep track of.

3 problems

Do congruent figures have to be the same size? 1 yes, 0 no.
Answer 1
Why That is what separates congruent from similar.
Angles of a triangle are 70 and 40. What is the third, in degrees?
Answer 70
Why They total 180.
Does the order of letters in a congruence statement matter? 1 yes, 0 no.
Answer 1
Why It states the correspondence.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Which transformations can be used to show congruence?
Answer Translation; Reflection; Rotation
Why One of these changes the size.
ABC congruent to DEF with angle C = 55°. What is angle F?
Answer 55
Why C matches F.
The Correspondence: Triangle ABC is congruent to triangle DEF, and AB = 5. What is DE?
Answer 5
Why 5.
The Angle: Same triangles, and angle B is 40°. What is angle E, in degrees?
Answer 40 degrees
Why 40°.