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Section 3.1 What Are Congruent Figures? Congruent Figures A non-geometry student may describe CONGRUENT triangles as having the same size and shape D A A geometry student would describe them as having 6 pairs of corresponding congruent parts: B F ◦ ◦ congruent angles congruent segments C E AB DF AC DE BC FE A D B F C E And therefore… ABC DFE Congruent Triangles Congruent triangles If all pairs of corresponding parts are S congruent, then X R XYZ TRS Y Z T X T Y R Z S XY TR YZ RS XZ TS Vocabulary Congruent Polygons All pairs of corresponding parts (angles and sides) are congruent. P A Q D B R C S A P, B Q, C R, D S AB PQ, BC QR, CD RS , and DA SP Parallelogram ABCD Parallelogram PQRS Caution ABC XYZ Be careful when naming congruent figures, C corresponding parts must be listed in the same order Y To check this, match up the vertices of the corresponding angles. Z X This notation means that BAC YXZ ABC XYZ BCA YZX B A and AB XY BC YZ CA ZX Caution Sometimes it is difficult to tell what parts of a congruent figure are congruent. To keep from making mistakes: Label your congruent sides and angles with tick marks and/or Use colored pencils ABC XYZ C Y X B A Z Reflexive Property Reflexive Property (Postulate) F Any figure or segment is congruent to itself Given the diagram as shown, what else do you need to know in order to say that FGH G H I FIH ? FH FH What property could we use to show this is true? The reflexive property, it says that any figure or segment is congruent to itself. Based on the markings on these triangles, NAME the congruent triangles correctly. O P 3 K B H A T 4 LM Y N OKL PMN MAT HTA C V A M W X D BAD BCD WVY WXZ Z Hints for finding congruent parts… Try and find out if your triangles are Reflections or Flips Translations or Slides Rotations or Turns Reflection (or Flip) A figure has been reflected if it has been flipped over a line. B E AB DE AC DF BC EF D A A D B E C F ABC DEF C F Translation (or Slide) The two figures shown are congruent. The correspondence is evident if we slide or translate one onto the other. O P S L LM PQ LO PS ON SR MN QR L P M Q N R O S M N Q LMNO PQRS R Rotation (or turn) A figure that has been rotated has been turned to form a congruent figure. Sometimes it is easier to see the corresponding parts if we rotate one onto the other. F FL KL FG KJ GL JL K L L F K G J J G L KLJ FLG K J Each pair of triangles is CONGRUENT. Do they 1 show a Reflection, Translation , or Rotation? 2 3 1 reflection 4 5 translation 9 8 rotation reflection 11 7 6 12 10 translation reflection REMEMBER…by definition… Corresponding Parts of Congruent Triangles are Congruent