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Transcript
Congruent figures 3.1 What Are Congruent Figures? Cade Levinson Pricci Honors Geometry 9 Part 1: Congruent • What is Congruent • Congruent figures have all sides and angles the same size and shape. • Therefore congruent can be defined as any figure with the same size and shape. • For example… Look! Flying Pie! Get it Pie! Pi! Math puns!!! These two triangles have the exact same size and shapes. Congruent triangles need to have all 6 parts (angles + sides) to be equal. This is true with the 2 above triangles. So triangle ABC is congruent to triangle DEF. But… Does that mean that triangle ABC is also congruent to triangle FED? NOOOOOO! The thing is… • When naming congruent figures, the points have to match up. Since point A is not equal to point F, triangle ABC would not equal Triangle FED. Polygons reflect! (Pikachu counters!) • Definition: Congruent polygons have all pairs of corresponding parts congruent. • Reflections of polygons are congruent since all of their parts are the same size and shape. • Each reflection also shares a similar part down the middle. Such as… These Ducks This leads to the Reflexive Property which states : Any segment or angle is congruent to itself. Sample Problem A E B D F C Given: E and F bisect segments AB and DC respectively. ABCD is a rectangle Are Parallelograms AEFD and EBCF congruent Since E and F bisect the segments those sides are congruent. In a triangle, the opposite sides and angles are congruent . Yes the two figures are congruent. Practice Problem • A B Triangle BFE C E F If E is the midpoint of segment CF, Triangle ACE is congruent to which other triangle? Works Cited • Rhoad, Richard, Milauskas George, and Whipple Robert. Geometry for Enjoyment and Challenge. Evanston: McDougal, Littell & Company, 1997. • Feliz, Mike. "Geometry 3.2 Congruent Triangles". Free Math Help. May 15 2008 <http://www.freemathhelp.com/felizcongruent-triangles.html>.