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Bell Work • A regular hexagon has a total perimeter of 120 inches. Find the measure of each side of the polygon. A hexagon has 6 sides. Since it’s a regular hexagon all of the sides are equal in length. 120 ÷ 6 = 20 inches Each side measures 20 inches. Identifying congruent figures • Two geometric figures are congruent if they have exactly the same size and shape. NOT CONGRUENT CONGRUENT Congruency • When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent. • What does congruent mean? Congruent means that they are the same or equal • What does the symbol look like? ≅ Triangles Corresponding angles A ≅ P B ≅ Q C ≅ R Corresponding Sides AB ≅ PQ BC ≅ QR CA ≅ RP B A Q CP R How do you write a congruence statement? • There is more than one way to write a congruence statement, but it is important to list the corresponding angles in the same order. Normally you would write ∆ABC ≅ ∆PQR, but you can also write that ∆BCA ≅ ∆QRP Ex. 1 Naming congruent parts • Write a congruence statement. ∆DEF ≅ ∆RST • Identify all parts of congruent corresponding parts. F R E S • Angles: D≅ R, E ≅ S, F ≅T • Sides DE ≅ RS, EF ≅ ST, FD ≅ TR D T Third Angle Theorem • If any two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent to one another. • If A ≅ D and B ≅ E, then C ≅ F. B Why does that work? C A E D F Ex. 3 Try this challenge! • In the diagram, N ≅ R and L ≅ S. From the Third Angles Theorem, you know that M ≅ T. So mM = mT. • Find the value of x. M (2x + 30)° T R 55° N 65° L S • From the Triangle Sum Theorem, mM=180° - 55° - 65° = 60° • mM = mT (2x + 30)° = 60° 2x = 30 x = 15 Ex. 2 • In the diagram NPLM ≅ EFGH • Find the value of y Hint: You know that N ≅ E. So, mN = mE. (7y + 9)° = 72° 7y = 63 y=9 F M 8m L G 110° (2x - 3) m 87° P (7y+9)° 72° 10 m N E H Practice