Each side measures 20 inches. 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.

CONGRUENT Triangles

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? What does the symbol look like? Congruent means that they are the same or equal ≅

Triangles Corresponding angles A ≅ P B ≅ Q C ≅ R Corresponding Sides AB ≅ PQ BC ≅ QR CA ≅ RP B Q R A C P

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. Identify all parts of congruent corresponding parts. ∆DEF ≅ ∆RST Angles: D≅ R, E ≅ S, F ≅T Sides DE ≅ RS, EF ≅ ST, FD ≅ TR

Why does that work? 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. Why does that work?

Ex. 3 Try this challenge! Find the value of x. In the diagram, N ≅ R and L ≅ S. From the Third Angles Theorem, you know that M ≅ T. So mM = mT. (2x + 30)° 55° 65° From the Triangle Sum Theorem, mM=180° - 55° - 65° = 60° mM = mT (2x + 30)° = 60° 2x = 30 x = 15

Ex. 2 Hint: You know that N ≅ E. So, mN = mE. In the diagram NPLM ≅ EFGH Find the value of y (7y + 9)° = 72° 7y = 63 y = 9 8 m 110° 87° 10 m 72° (7y+9)° (2x - 3) m

Practice