What is the difference between similar and congruent triangles?

Similar triangles have the same shape but different sizes, while congruent triangles are identical in both shape and size.

If two triangles have all three angles identical, are they necessarily congruent? Explain your answer.

No, they are not necessarily congruent. They are similar. Congruence requires the sides to be identical as well.

Explain the Side-Angle-Side (SAS) theorem for proving triangle congruence.

If two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.

Can the Angle-Angle-Angle (AAA) theorem be used to prove congruence? Why or why not?

No, the Angle-Angle-Angle (AAA) theorem cannot be used to prove congruence because it only proves similarity.

Creating Geometry Proofs Lesson Plan for Grade 10

Lesson Preview

Learning Objective

I can construct a geometric proof using theorems and postulates.

1
Two triangles are said to be similar if they have the same shape but different sizes, and congruent if they are absolutely identical.
2
The Side-Side-Side theorem states that if all three sides of one triangle are identical to the corresponding sides of another triangle, the two triangles must be congruent.
3
The Angle-Side-Angle theorem states that if a side and the two adjacent angles are identical to those of another triangle, the two triangles must be congruent.

Creating Geometry Proofs

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Learning Objective

Warm-Up Video

Key Concepts

Practice Questions

Exit Ticket

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