Warm-Up What are our two definitions of congruent?

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Presentation transcript:

Warm-Up What are our two definitions of congruent? Two figures are congruent if an isometry or composition of isometries maps one figure onto the other. Two figures that are the same shape are congruent if their corresponding sides and corresponding angles are congruent.

Warm-Up What do isometries preserve? Angle measures and side lengths.

4.2 and 4.3 Congruent Triangles and SSS Using rigid motion transformations and constructions to show triangles are congruent Objectives: To define congruent triangles To write a congruent statement To prove triangles congruent by SSS

Congruent Triangles (CPCTC) Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent. Corresponding sides are congruent Corresponding angles are congruent

Congruence Statement When naming two congruent triangles, order is very important.

Example 1 Which polygon is congruent to ABCDE? ABCDE  -?-

Example 2 Locate points I and S so that BLUE  FISH. S I

Copying a Segment We’re going to try making two congruent triangles by simply copying the three sides using only a compass and a straightedge. First, remember how to copy a segment.

Copying a Segment Draw segment AB.

Copying a Segment Draw a line with point A’ on one end.

Copying a Segment Put point of compass on A and the pencil on B. Make a small arc.

Copying a Segment Put point of compass on A’ and use the compass setting from Step 3 to make an arc that intersects the line. This is B’.

Investigation 1 Now apply the construction for copying a segment to copy the three sides of a triangle.

Investigation 1 Use your straight edge to construct a triangle. Now draw a line with A’ on one end.

Investigation 1 Copy segment AB onto your line to make A’B’.

Investigation 1 Put point of compass on A and pencil on C. Copy this distance from A’.

Investigation 1 Put point of compass on B and pencil on C. Copy this distance from B’. This is C’

Investigation 1 Finish your new triangle by drawing segments A’C’ and B’C’.

Investigation 1 Copy the original triangle ABC onto a piece of patty paper. Compare this triangle to triangle A’B’C’. Are they congruent?

Side-Side-Side Congruence Postulate SSS Congruence Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

SSS Congruence Postulate

Example 3 Decide whether the triangles are congruent. Explain your reasoning.