4-1 Congruent Figures

SWBAT:Recognize Congruent Figures and Their

Corresponding Parts

Recall…• What are Congruent Segments?

• What are Congruent Angles?

We know that Congruent Segments have the equal lengths and Congruent Angles have the equal angle measure.

• Predict what you think Congruent Figures are…

Congruent Figures• Congruent Figures have the same size and

shape.• When two figures are congruent, you can

move one so it fits exactly on top of another one.

• Three ways to do this are a slide, flip, and/or a turn.

What are Congruent Polygons?

• Congruent polygons have congruent corresponding sides and angles.

• Matching Vertices are Corresponding Vertices.

• When you name congruent polygons, always list the corresponding vertices in the same order.

Listing Corresponding Parts

Name the Corresponding Angles…

Name The Corresponding Sides…

• If we can say all corresponding sides and angles are congruent, then we can say the polygons are congruent.

• It is very important when you write a congruence statement, that the corresponding angles are in the same position in the statement:

• What is another way to write the statement?

Ex 1: Naming Congruent Parts

Ex 1B: No Diagram? No Problem!

Given the following Congruence Statement, list the congruent corresponding parts.

Sides: Angles:

Ex 2: Congruent Triangles?

Prove that the triangles are congruent. Justify your answer. Sides:

Angles:

Apply your knowledge

• Nothing is more exciting than proofs!!! Let’s try a proof that utilizes this theorem.

4. Two corresponding angle pairs are ≅ so we know the third pair is ≅…

ClosureSuppose that two pentagons are congruent. How many pairs of corresponding parts are there? Explain.    Suppose that two hexagons are congruent. How many pairs of corresponding parts are there? Explain.   Suppose that two n-gons are congruent. How can we represent how many pairs of corresponding parts are there? Explain.