Warm up (TI)

1. Warm up (TI) Find the measure of each angle of the triangles given below. Then classify the triangle by its angles. • m<A = 2x + 5, m<B = 3x – 15, m<C = 4x + 10. • m<K = 10(x + 1), m<L = 9x – 3, m<M = 7x – 9.

2. Congruence and Triangles Chapter 4 Section 2

3. Congruent Figures • Two geometric figures are congruent if they have the same size and shape. • Same size implies same side lengths. • Same shape implies same angle measures.

4. Corresponding parts.. • When two figures are congruent, their corresponding angles are congruent and their corresponding sides are congruent. ~ ∆ABC = ∆DEF D A F B C E

5. Examples • Write a congruence statement for the triangles below. Identify all pairs of corresponding parts. Y H K Z X J

6. Example ~ • In the diagram, ABCD = KJHL • Find the value of x. • Find the value of y. K A 9 cm B L 91° 4x - 3 5y - 12 86° 113° D C H J 6 cm

7. Third Angle Theorem • If two angles of a triangle are congruent to two angles of another triangle, then the third angles are also congruent.

8. Example • Find the value of x. 4x + 15 87° 22°

9. Are these triangles congruent? If so…write a congruence statement. • Ask yourself…Are all corresponding parts congruent? • Is there anything that I can add to the diagram…(you must be able to justify anything that you add!) 21 4 21 4

10. Properties of Congruent Triangles • Reflexive property: Every triangle is congruent to itself. • Symmetric property: If ∆ABC = ∆DEF then ∆DEF = ∆ABC. • Transitive property: If ∆ABC = ∆DEF and ∆DEF = ∆JKL, then ∆ABC = ∆JKL. ~ ~ ~ ~ ~

11. Example • Given MN = QP, MN PQ, O is the midpoint of MQ and PN. • How do we know that ∆MNO = ∆QPO? ~ ~ M N O Q P

12. Are there congruent triangles in this picture? If so write a congruence statement! A D B C

13. Assignment Complete assignment 2 and notecards!