Warm up (distance, midpoint, slope) 1.The coordinates of the midpoint of AB are (4,-2), and the coordinates of B are (6,8). What are the coordinates of A? 2.Find the distance between points M and N where M(6,-8) and N(-2,15)? 3. What is the slope of the line perpendicular to the line containing points (6,-8) and (-2,4)? 4. What is the midpoint of (2,4) and (15,3)?

Exploring Congruent Triangles Sec: 4.2 Sol:G.4a

Congruent triangles: Triangles that are the same size and shape – Each triangle has six parts, three angles and three sides – If the corresponding six parts of one triangle are congruent to the six parts of another triangle, then the triangles are congruent This is abbreviated by CPCTC (corresponding parts of congruent triangles are congruent) – Orientation of the triangles is not important. This means that the triangles can be flipped, slid and turned around, and if the corresponding parts are congruent, the triangles are congruent

Segments: Angles: Note: The order matters. If  ABC   DEF, it is not the same as saying  ABC   FED.

EXAMPLE: If  ABC   RQC, name the corresponding congruent sides and angles. Congruent Sides – Congruent Angles –

In the design above, indicate which triangles appear to be congruent (Remember, order of letters matters!)

Congruence of triangles is: Reflexive:  ABC   ABC

Congruence of triangles is: Symmetric If  ABC   EFD, then  EFD   ABC

Congruence of triangles is: Transitive If  ABC   EFD and  EFD   HIG, then  ABC   HIG.

Identify Congruence Transformations:

Transformations in the coordinate plane: The vertices of triangle STR are: S(0, 5), T(1, 1), R(-3, 0) The vertices of triangle S’T’R’ are: S’(0, -5), T’(-1, -1), R’(3, 0) Verify that the two triangles are congruent. Step 1: Graph Step 2: Use the distance formula to find the length of the sides.

Assignments Classwork: Blue Handout on Triangle Congruency Homework: pg