grade 8-third Triangle Congruence...pptx

triangle Congruence

1. If you slide the pink triangle to the right, in which color will it fit in?

2. If you slide the green triangle to the right, in which color will it fit in?

3. If you flip the blue triangle, in which color will it fit in?

4. CONGRUENCE Means having the same shape and size, and it is denoted by . The top part of the symbol,∼, is the sign for similarity and indicates the same shape. The bottom part symbol, = , is the sign of equality and indicates the same size.  

5. Idea of Congruence

6. Idea of CONGRUENCE The idea of congruence always helps to recognize congruent figures in the same orientation. When two figures are congruent, you may slide, flip, rotate the figures until they overlap exactly.

7. Properties of TRIANGLE CONGRUENCE The properties of equality as well as the properties of congruence that follow from them are often used in doing formal geometric proof. REFLEXIVE PROPERTY OF CONGRUENCE SYMMETRIC PROPERTY OF CONGRUENCE TRANSITIVE PROPERTY OF CONGRUENCE   If   If If  

8. If ∆ABC slides over to the right to fit in ∆JKL, they will fit exactly. However, they will fit exactly only if a proper pairing of the vertices is made. In this case, the proper pairing will have to be: A to J or A ↔ J read as “ A corresponds to J.” B to K or B ↔ K read as “ B corresponds to K.” C to L or C ↔ L read as “ C corresponds to L.” A B C K J L When the vertices are matched this way, are corresponding angles and AC and JL are corresponding sides .   Corresponding angles and corresponding sides are examples of corresponding parts. Figures are congruent if all pairs of corresponding sides and angles are congruent.

9. The correspondence among vertices can be used to name the corresponding congruent sides and angles of the two triangles.   If two triangles are congruent, then their corresponding parts are also congruent. (Corresponding Parts of Congruent Triangles are Congruent) or CPCTC. Two polygons are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent.  

10. CONGRUENT TRIANGLES Two triangles are congruent if and only if their corresponding parts are congruent.   Then, ∆ABC     A B C P Q R