1. 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.

2. CONGRUENT
Triangles

3. Identifying congruent figures
Two geometric figures are congruent if they have exactly the same size and shape.
NOT CONGRUENT
CONGRUENT

4. 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 ≅

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

6. 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

7. 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

8. 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?

9. 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

10. 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

11. Practice